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commit e9cab2ce52577297627729b31f768a116da2402b
Author: buildbot <[email protected]>
AuthorDate: Fri Jul 29 03:02:09 2022 +0000
Automatic Site Publish by Buildbot
---
.../SketchingQuantilesAndRanksTutorial.html | 44 ++++++++++++++++++++--
1 file changed, 40 insertions(+), 4 deletions(-)
diff --git a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
index 81d3b82a..ff8d07ca 100644
--- a/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
+++ b/output/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html
@@ -726,7 +726,18 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
<h3 id="the-non-inclusive-criterion-for-rq-aka-the-lt-criterion">The
<strong><em>non inclusive</em></strong> criterion for
<strong><em>r(q)</em></strong> (a.k.a. the <strong><em>LT</em></strong>
criterion):</h3>
-<p>Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 < q <= q2</em>. Return the rank associated
with <em>q1</em>, the first of the pair.</p>
+<p><b>Definition:</b>
+Given <em>q</em>, return the rank, <em>r</em>, of the largest quantile that is
strictly less than <em>q</em>.</p>
+
+<p><b>Implementation:</b>
+Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 < q <= q2</em>. Return the rank,
<em>r</em>, associated with <em>q1</em>, the first of the pair.</p>
+
+<p><b>NOTES:</b></p>
+
+<ul>
+ <li>If the given <em>q</em> is larger than the largest quantile retained by
the sketch, the sketch will return the rank of the largest retained
quantile.</li>
+ <li>If the given <em>q</em> is smaller than the smallest quantile retained
by the sketch, the sketch will return a rank of zero.</li>
+</ul>
<p>For example <em>q = 30; r(30) = 5</em></p>
@@ -761,7 +772,18 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
<h3 id="the-inclusive-criterion-for-rq-aka-the-le-criterion">The
<strong><em>inclusive</em></strong> criterion for
<strong><em>r(q)</em></strong> (a.k.a. the <strong><em>LE</em></strong>
criterion):</h3>
-<p>Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 <= q < q2</em>. Return the rank associated
with <em>q1</em>, the first of the pair.</p>
+<p><b>Definition:</b>
+Given <em>q</em>, return the rank, <em>r</em>, of the largest quantile that is
less than or equal to <em>q</em>.</p>
+
+<p><b>Implementation:</b>
+Given <em>q</em>, search the quantile array until we find the adjacent pair
<em>{q1, q2}</em> where <em>q1 <= q < q2</em>. Return the rank,
<em>r</em>, associated with <em>q1</em>, the first of the pair.</p>
+
+<p><b>NOTES:</b></p>
+
+<ul>
+ <li>If the given <em>q</em> is larger than the largest quantile retained by
the sketch, the sketch will return the rank of the largest retained
quantile.</li>
+ <li>If the given <em>q</em> is smaller than the smallest quantile retained
by the sketch, the sketch will return a rank of zero.</li>
+</ul>
<p>For example <em>q = 30; r(30) = 11</em></p>
@@ -798,7 +820,17 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
<h3 id="the-non-inclusive-criterion-for-qr-aka-the-gt-criterion">The
<strong><em>non inclusive</em></strong> criterion for
<strong><em>q(r)</em></strong> (a.k.a. the <strong><em>GT</em></strong>
criterion):</h3>
-<p>Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 <= r < r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
+<p><b>Definition:</b>
+Given <em>r</em>, return the quantile of the smallest rank that is strictly
greater than <em>r</em>.</p>
+
+<p><b>Implementation:</b>
+Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 <= r < r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
+
+<p><b>NOTES:</b></p>
+
+<ul>
+ <li>If the given normalized rank, <em>r</em>, is equal to 1.0, there is no
quantile that satisfies this criterion. This function may choose to return
either a <em>NaN</em> value, or return the largest quantile retained by the
sketch.</li>
+</ul>
<p>For example <em>r = 5; q(5) = 30</em></p>
@@ -833,7 +865,11 @@ the function <em>r(q)</em> is ambiguous. We will see how
to resolve this shortly
<h3 id="the-inclusive-criterion-for-qr--aka-the-ge-criterion">The
<strong><em>inclusive</em></strong> criterion for
<strong><em>q(r)</em></strong> (a.k.a. the <strong><em>GE</em></strong>
criterion):</h3>
-<p>Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 < r <= r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
+<p><b>Definition:</b>
+Given <em>r</em>, return the quantile of the smallest rank that is strictly
greater than or equal to <em>r</em>.</p>
+
+<p><b>Implementation:</b>
+Given <em>r</em>, search the rank array until we find the adjacent pair
<em>{r1, r2}</em> where <em>r1 < r <= r2</em>. Return the quantile
associated with <em>r2</em>, the second of the pair.</p>
<p>For example <em>q(11) = 30</em></p>
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