Repository navigation
Expand file tree
/
Copy pathdip-FastVarianceAccumulator.html
More file actions
246 lines (245 loc) · 16.8 KB
/
Copy pathdip-FastVarianceAccumulator.html
File metadata and controls
246 lines (245 loc) · 16.8 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<title>dip::FastVarianceAccumulator class | DIPlib | a library for quantitative image analysis</title>
<link rel="stylesheet" href="m-dip+documentation.compiled.css" />
<link rel="icon" href="DIPlib_logo_32.png" type="image/png" />
<link rel="search" type="application/opensearchdescription+xml" href="opensearch.xml" title="Search DIPlib documentation" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="theme-color" content="#ffffff" />
</head>
<body>
<header><nav id="navigation">
<div class="m-container">
<div class="m-row">
<span id="m-navbar-brand" class="m-col-t-8 m-col-m-none m-left-m">
<a href="https://diplib.org"><img src="DIPlib_logo.svg" alt="" />DIPlib</a><span class="m-breadcrumb">┃</span><a href="index.html" class="m-thin">a library for quantitative image analysis</a><span class="m-breadcrumb">┃</span><a href="https://github.com/DIPlib/diplib/releases/tag/3.6.1" class="m-thin">version 3.6.1</a> </span>
<div class="m-col-t-4 m-hide-m m-text-right m-nopadr">
<a href="#search" class="m-doc-search-icon" title="Search" onclick="return showSearch()"><svg style="height: 0.9rem;" viewBox="0 0 16 16">
<path id="m-doc-search-icon-path" d="m6 0c-3.31 0-6 2.69-6 6 0 3.31 2.69 6 6 6 1.49 0 2.85-0.541 3.89-1.44-0.0164 0.338 0.147 0.759 0.5 1.15l3.22 3.79c0.552 0.614 1.45 0.665 2 0.115 0.55-0.55 0.499-1.45-0.115-2l-3.79-3.22c-0.392-0.353-0.812-0.515-1.15-0.5 0.895-1.05 1.44-2.41 1.44-3.89 0-3.31-2.69-6-6-6zm0 1.56a4.44 4.44 0 0 1 4.44 4.44 4.44 4.44 0 0 1-4.44 4.44 4.44 4.44 0 0 1-4.44-4.44 4.44 4.44 0 0 1 4.44-4.44z"/>
</svg></a>
<a id="m-navbar-show" href="#navigation" title="Show navigation"></a>
<a id="m-navbar-hide" href="#" title="Hide navigation"></a>
</div>
<div id="m-navbar-collapse" class="m-col-t-12 m-show-m m-col-m-none m-right-m">
<div class="m-row">
<ol class="m-col-t-6 m-col-m-none">
<li><a href="pages.html">Pages</a></li>
<li><a href="modules.html">Modules</a></li>
</ol>
<ol class="m-col-t-6 m-col-m-none" start="3">
<li><a href="classes.html">Classes</a></li>
<li><a href="files.html">Files</a></li>
<li class="m-show-m"><a href="#search" class="m-doc-search-icon" title="Search" onclick="return showSearch()"><svg style="height: 0.9rem;" viewBox="0 0 16 16">
<use href="#m-doc-search-icon-path" />
</svg></a></li>
</ol>
</div>
</div>
</div>
</div>
</nav></header>
<main><article>
<div class="m-container m-container-inflatable">
<div class="m-row">
<div class="m-col-l-10 m-push-l-1">
<h1>
<div class="m-doc-include m-thin m-right-m m-text-right">
<a href="numeric.html" class="m-doc">Numeric algorithms and constants</a> module<br/><span class="m-code m-thin">#include <a href="file--diplib--accumulators-h.html">"diplib/accumulators.h"</a></span> </div>
<span class="m-breadcrumb"><a href="dip.html">dip</a>::<wbr/></span>FastVarianceAccumulator <span class="m-thin">class</span> </h1>
<p><code>FastVarianceAccumulator</code> computes mean and standard deviation by accumulating the sum of sample
values and the sum of the square of sample values.</p>
<div class="m-index m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#function-members">Functions</a></li>
<li><a href="#operator-members">Operators</a></li>
<li><a href="#related">Related</a></li>
</ul>
</li>
</ul>
</div>
<p>Samples are added one by one, using the <code>Push</code> method. Other members are used to retrieve estimates of
the population statistics based on the samples seen up to that point. Formula used to compute population
statistics are corrected, though the standard deviation is not an unbiased estimator. The accumulator
uses a simple algorithm that could result in catastrophic cancellation if the variance is very small with
respect to the mean; use <a href="dip-VarianceAccumulator.html"><code>dip::VarianceAccumulator</code></a> to prevent it.</p>
<p>It is possible to accumulate samples in different objects (e.g. when processing with multiple threads),
and add the accumulators together using the <code>+</code> operator.</p>
<p>It is also possible to remove a sample from the accumulator, using the <code>Pop</code> method. It is assumed that the
particular value passed to this method had been added previously to the accumulator. If this is not the case,
resulting means and variances are no longer correct.</p>
<aside class="m-note m-default">
<h4>See also</h4>
<p><a href="dip-StatisticsAccumulator.html"><code>dip::StatisticsAccumulator</code></a>, <a href="dip-VarianceAccumulator.html"><code>dip::VarianceAccumulator</code></a>, <a href="dip-CovarianceAccumulator.html"><code>dip::CovarianceAccumulator</code></a>, <a href="dip-DirectionalStatisticsAccumulator.html"><code>dip::DirectionalStatisticsAccumulator</code></a>, <a href="dip-MinMaxAccumulator.html"><code>dip::MinMaxAccumulator</code></a>, <a href="dip-MomentAccumulator.html"><code>dip::MomentAccumulator</code></a></p>
</aside>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FastVarianceAccumulator-Mean-C" class="m-doc">Mean</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Unbiased estimator of population mean</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FastVarianceAccumulator-Number-C" class="m-doc">Number</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Number of samples</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-FastVarianceAccumulator-Pop-dfloat-" class="m-doc">Pop</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> x)</span>
</dt>
<dd>Remove a sample from the accumulator</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-FastVarianceAccumulator-Push-dfloat-" class="m-doc">Push</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> x)</span>
</dt>
<dd>Add a sample to the accumulator</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-FastVarianceAccumulator-Reset" class="m-doc">Reset</a>(</span><span class="m-doc-wrap">)</span>
</dt>
<dd>Reset the accumulator, leaving it as if newly allocated.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FastVarianceAccumulator-StandardDeviation-C" class="m-doc">StandardDeviation</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Estimator of population standard deviation (it is not possible to derive an unbiased estimator)</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FastVarianceAccumulator-Variance-C" class="m-doc">Variance</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Unbiased estimator of population variance</dd>
</dl>
</section>
<section id="operator-members">
<h2>Operators</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-FastVarianceAccumulator-operator%2B%3D-FastVarianceAccumulator-CL" class="m-doc">operator+=</a>(</span><span class="m-doc-wrap"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> const& b) -> <a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a>&</span>
</dt>
<dd>Combine two accumulators</dd>
</dl>
</section>
<section id="related">
<h2>Related</h2>
<dl class="m-doc">
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-operator%2B-FastVarianceAccumulator--FastVarianceAccumulator-CL" class="m-doc">dip::<wbr />operator+</a>(</span><span class="m-doc-wrap"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> lhs,
<a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> const& rhs) -> <a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a></span>
</dt>
<dd>Combine two accumulators</dd>
</dl>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Reset"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Reset" class="m-doc-self">Reset</a></span>(
) </h3>
<p>Reset the accumulator, leaving it as if newly allocated.</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Push-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Push-dfloat-" class="m-doc-self">Push</a></span>(
<span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> x</span>) </h3>
<p>Add a sample to the accumulator</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Pop-dfloat-"><div>
<h3>
<span class="m-doc-return">void </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Pop-dfloat-" class="m-doc-self">Pop</a></span>(
<span class="m-doc-arg"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> x</span>) </h3>
<p>Remove a sample from the accumulator</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Number-C"><div>
<h3>
<span class="m-doc-return"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Number-C" class="m-doc-self">Number</a></span>(
) const </h3>
<p>Number of samples</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Mean-C"><div>
<h3>
<span class="m-doc-return"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Mean-C" class="m-doc-self">Mean</a></span>(
) const </h3>
<p>Unbiased estimator of population mean</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-Variance-C"><div>
<h3>
<span class="m-doc-return"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-Variance-C" class="m-doc-self">Variance</a></span>(
) const </h3>
<p>Unbiased estimator of population variance</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-StandardDeviation-C"><div>
<h3>
<span class="m-doc-return"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-StandardDeviation-C" class="m-doc-self">StandardDeviation</a></span>(
) const </h3>
<p>Estimator of population standard deviation (it is not possible to derive an unbiased estimator)</p>
</div></section>
<section class="m-doc-details" id="dip-FastVarianceAccumulator-operator%2B%3D-FastVarianceAccumulator-CL"><div>
<h3>
<span class="m-doc-return"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a>& </span>
<span class="m-doc-name"><a href="#dip-FastVarianceAccumulator-operator%2B%3D-FastVarianceAccumulator-CL" class="m-doc-self">operator+=</a></span>(
<span class="m-doc-arg"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> const& b</span>) </h3>
<p>Combine two accumulators</p>
</div></section>
<section class="m-doc-details" id="dip-operator%2B-FastVarianceAccumulator--FastVarianceAccumulator-CL"><div>
<h3>
<span class="m-doc-return"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> </span>
<span class="m-doc-name"><a href="#dip-operator%2B-FastVarianceAccumulator--FastVarianceAccumulator-CL" class="m-doc-self">dip::<wbr />operator+</a></span>(
<span class="m-doc-arg"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> lhs, </span><span class="m-doc-arg"><a href="dip-FastVarianceAccumulator.html" class="m-doc">dip::FastVarianceAccumulator</a> const& rhs</span>) </h3>
<p>Combine two accumulators</p>
</div></section>
</section>
</div>
</div>
</div>
</article></main>
<div class="m-doc-search" id="search">
<a href="#!" onclick="return hideSearch()"></a>
<div class="m-container">
<div class="m-row">
<div class="m-col-m-8 m-push-m-2">
<div class="m-doc-search-header m-text m-small">
<div><span class="m-label m-default">Tab</span> / <span class="m-label m-default">T</span> to search, <span class="m-label m-default">Esc</span> to close</div>
<div id="search-symbolcount">…</div>
</div>
<div class="m-doc-search-content">
<form action="https://diplib.org/diplib-docs/#search">
<input type="search" name="q" id="search-input" placeholder="Loading …" disabled="disabled" autofocus="autofocus" autocomplete="off" spellcheck="false" />
</form>
<noscript class="m-text m-danger m-text-center">Unlike everything else in the docs, the search functionality <em>requires</em> JavaScript. Enable it or <a href="https://google.com/search?q=site:diplib.org+">use an external search engine</a>.</noscript>
<div id="search-help" class="m-text m-dim m-text-center">
<p class="m-noindent">Search for symbols, directories, files, pages or modules.
You can omit any prefix from the symbol or file path; adding a <code>:</code> or
<code>/</code> suffix lists all members of given symbol or directory.</p>
<p class="m-noindent">Use <span class="m-label m-dim">↓</span> / <span class="m-label m-dim">↑</span> to navigate through the list,
<span class="m-label m-dim">Enter</span> to go.
<span class="m-label m-dim">Tab</span> autocompletes common prefix.
You can copy a link to the result using <span class="m-label m-dim">⌘</span> <span class="m-label m-dim">L</span>,
or <span class="m-label m-dim">⌘</span> <span class="m-label m-dim">M</span> to copy a Markdown link.</p>
</div>
<div id="search-notfound" class="m-text m-warning m-text-center">Sorry, nothing was found.<br />Maybe try a full-text <a href="#" id="search-external" data-search-engine="https://google.com/search?q=site:diplib.org+{query}">search with external engine</a>?</div>
<ul id="search-results"></ul>
</div>
</div>
</div>
</div>
</div>
<script src="search-v1.js"></script>
<script src="searchdata-v1.js" async="async"></script>
<footer><nav>
<div class="m-container">
<div class="m-row">
<div class="m-col-l-10 m-push-l-1">
<p>DIPlib, a library for quantitative image analysis. Documentation compiled with <a href="https://crisluengo.github.io/doxpp/">dox++</a> and styled with <a href="https://mcss.mosra.cz/">m.css</a>.</p>
</div>
</div>
</div>
</nav></footer>
</body>
</html>