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dip-Distribution.html
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<!DOCTYPE html>
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<title>dip::Distribution class | DIPlib | a library for quantitative image analysis</title>
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<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/3.5.1" class="m-thin">version 3.5.1</a> </span>
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<h1>
<div class="m-doc-include m-right-m m-text-right">
<span class="m-thin"><a href="analysis.html" class="m-doc">Analysis</a> module</span><br/><span class="m-code m-inverted"><span class="cp">#include</span> <a class="cpf" href="file--diplib--distribution-h.html">"diplib/distribution.h"</a></span> </div>
<span class="m-breadcrumb"><a href="dip.html">dip</a>::<wbr/></span>Distribution <span class="m-thin">class</span> </h1>
<p>Holds probability density functions and other types of distribution</p>
<div class="m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#typeless-methods">Constructors, destructors, assignment and conversion operators</a></li>
<li><a href="#nested-classes">Classes</a></li>
<li><a href="#alias-members">Aliases</a></li>
<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>
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<p>This is a container class to hold results of certain type of analysis that compute
a property as a function of scale or intensity. Even though a histogram could fit
within this description, the <a href="dip-Histogram.html"><code>dip::Histogram</code></a> class is specifically meant to
hold histograms, and purposefully kept separate from this class. A <code>dip::Histogram</code>
with a 1D histogram can be cast to a <code>dip::Distribution</code>.</p>
<p>Distributions represent a function <em>y</em> of <em>x</em>, where <em>x</em> is not necessarily uniformly
spaced. Both <em>x</em> and <em>y</em> are stored as double-precision floating point values.
The distribution can also be a multi-valued function, with multiple <em>y</em> values for
every <em>x</em> value. In this case, the <em>y</em> values for each <em>x</em> are arranged as a 2D matrix
<em>NxM</em>, where <em>M</em> is 1 for a vector-like set of values.</p>
<p>Elements can be modified in such a way that <em>x</em> is no longer sorted.
The <code>Sort</code> method applies a stable sort to restore the order.</p>
<section id="typeless-methods">
<h2>Constructors, destructors, assignment and conversion operators</h2>
<dl class="m-doc">
<dt id="dip-Distribution-Distribution-dip-uint--dip-uint--dip-uint-">
<span class="m-doc-wrap-bumper"><a href="#dip-Distribution-Distribution-dip-uint--dip-uint--dip-uint-" class="m-doc-self">Distribution</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> size = 0,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rows = 1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> columns = 1) <span class="m-label m-flat m-info">explicit</span> </span>
</dt>
<dd>A zero-initialized distribution can be created by giving a size, and number of values (or rows and columns) per sample</dd>
<dt id="dip-Distribution-Distribution-std-vector<dfloat>-CL-dip-uint--dip-uint-">
<span class="m-doc-wrap-bumper"><a href="#dip-Distribution-Distribution-std-vector<dfloat>-CL-dip-uint--dip-uint-" class="m-doc-self">Distribution</a>(</span><span class="m-doc-wrap">std::vector<dfloat> const& x,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> rows = 1,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> columns = 1) <span class="m-label m-flat m-info">explicit</span> </span>
</dt>
<dd>A zero-initialized distribution can be created by giving an array of the <em>x</em> values, and number of values (or rows and columns) per sample</dd>
<dt id="dip-Distribution-Distribution-std-vector<dfloat>-CL-std-vector<dfloat>-CL">
<span class="m-doc-wrap-bumper"><a href="#dip-Distribution-Distribution-std-vector<dfloat>-CL-std-vector<dfloat>-CL" class="m-doc-self">Distribution</a>(</span><span class="m-doc-wrap">std::vector<dfloat> const& x,
std::vector<dfloat> const& y)</span>
</dt>
<dd>A distribution can be created by giving an array of the <em>x</em> values and an array of the <em>y</em> values</dd>
<dt id="dip-Distribution-Distribution-Histogram-CL">
<span class="m-doc-wrap-bumper"><a href="#dip-Distribution-Distribution-Histogram-CL" class="m-doc-self">Distribution</a>(</span><span class="m-doc-wrap"><a href="dip-Histogram.html" class="m-doc">dip::Histogram</a> const& histogram)</span>
</dt>
<dd>A 1D <a href="dip-Histogram.html"><code>dip::Histogram</code></a> can be cast to a <code>dip::Distribution</code></dd>
</dl>
</section>
<section id="nested-classes">
<h2>Classes</h2>
<dl class="m-doc">
<dt>
class <a href="dip-Distribution-Sample.html" class="m-doc">Sample</a>
</dt>
<dd>One sample of a distribution.</dd>
<dt>
class <a href="dip-Distribution-ConstSample.html" class="m-doc">ConstSample</a>
</dt>
<dd>One unmutable sample of a distribution, see <a href="dip-Distribution-Sample.html"><code>dip::Distribution::Sample</code></a> for details.</dd>
<dt>
<div class="m-doc-template">template<typename T></div>
class <a href="dip-Distribution-IteratorTemplate-T.html" class="m-doc">IteratorTemplate</a>
</dt>
<dd>An iterator for <code>dip::Distribution</code>. Dereferences into a <code>Sample</code> or a <code>ConstSample</code> (the value of <code>T</code>).</dd>
</dl>
</section>
<section id="alias-members">
<h2>Aliases</h2>
<dl class="m-doc">
<dt id="dip-Distribution-ValueType">
using <a href="#dip-Distribution-ValueType" class="m-doc-self">ValueType</a> = <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a>
</dt>
<dd>Data type of values stored in container</dd>
<dt id="dip-Distribution-Container">
using <a href="#dip-Distribution-Container" class="m-doc-self">Container</a> = std::vector<ValueType>
</dt>
<dd>Container used internally to store the data</dd>
<dt id="dip-Distribution-Iterator">
using <a href="#dip-Distribution-Iterator" class="m-doc-self">Iterator</a> = <a href="dip-Distribution-IteratorTemplate-T.html" class="m-doc">dip::Distribution::IteratorTemplate</a>
</dt>
<dd>An iterator for <code>dip::Distribution</code>. Dereferences into a <code>Sample</code>.</dd>
<dt id="dip-Distribution-ConstIterator">
using <a href="#dip-Distribution-ConstIterator" class="m-doc-self">ConstIterator</a> = <a href="dip-Distribution-IteratorTemplate-T.html" class="m-doc">dip::Distribution::IteratorTemplate</a>
</dt>
<dd>An iterator for <code>const dip::Distribution</code>. Dereferences into a <code>ConstSample</code>.</dd>
</dl>
</section>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt id="dip-Distribution-Empty-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Empty-C" class="m-doc-self">Empty</a>(</span><span class="m-doc-wrap">) const -> bool <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Checks whether the distribution is empty (size is 0)</dd>
<dt id="dip-Distribution-Size-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Size-C" class="m-doc-self">Size</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns the size of the distribution (number of data points)</dd>
<dt id="dip-Distribution-ValuesPerSample-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-ValuesPerSample-C" class="m-doc-self">ValuesPerSample</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Returns the number of <em>y</em> values per sample</dd>
<dt id="dip-Distribution-Rows-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Rows-C" class="m-doc-self">Rows</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Returns the number of rows in the matrix of <em>y</em> values</dd>
<dt id="dip-Distribution-Columns-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Columns-C" class="m-doc-self">Columns</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Returns the number of columns in the matrix of <em>y</em> values</dd>
<dt id="dip-Distribution-XUnits-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-XUnits-C" class="m-doc-self">XUnits</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-Units.html" class="m-doc">dip::Units</a> const&</span>
</dt>
<dd>Returns the units used along the <em>x</em> axis.</dd>
<dt id="dip-Distribution-XUnits">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-XUnits" class="m-doc-self">XUnits</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Units.html" class="m-doc">dip::Units</a>&</span>
</dt>
<dd>Returns a modifiable reference to the units used along the <em>x</em> axis.</dd>
<dt id="dip-Distribution-Back">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Back" class="m-doc-self">Back</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution-Sample.html" class="m-doc">dip::Distribution::Sample</a></span>
</dt>
<dd>Gets the <em>x</em> and <em>y</em> values at the end</dd>
<dt id="dip-Distribution-Back-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Back-C" class="m-doc-self">Back</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-Distribution-ConstSample.html" class="m-doc">dip::Distribution::ConstSample</a></span>
</dt>
<dd>Gets the <em>x</em> and <em>y</em> values at the end</dd>
<dt id="dip-Distribution-begin">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-begin" class="m-doc-self">begin</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html#dip-Distribution-Iterator" class="m-doc">dip::Distribution::Iterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an iterator to the beginning</dd>
<dt id="dip-Distribution-begin-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-begin-C" class="m-doc-self">begin</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-Distribution.html#dip-Distribution-ConstIterator" class="m-doc">dip::Distribution::ConstIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an iterator to the beginning</dd>
<dt id="dip-Distribution-end">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-end" class="m-doc-self">end</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html#dip-Distribution-Iterator" class="m-doc">dip::Distribution::Iterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an iterator to the end</dd>
<dt id="dip-Distribution-end-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-end-C" class="m-doc-self">end</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-Distribution.html#dip-Distribution-ConstIterator" class="m-doc">dip::Distribution::ConstIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an iterator to the end</dd>
<dt id="dip-Distribution-Xbegin">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Xbegin" class="m-doc-self">Xbegin</a>(</span><span class="m-doc-wrap">) -> <a href="dip-SampleIterator-T.html" class="m-doc">dip::SampleIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an <em>x</em>-value iterator to the beginning</dd>
<dt id="dip-Distribution-Xbegin-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Xbegin-C" class="m-doc-self">Xbegin</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-SampleIterator-T.html#dip-ConstSampleIterator-T" class="m-doc">dip::ConstSampleIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an <em>x</em>-value iterator to the beginning</dd>
<dt id="dip-Distribution-Xend">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Xend" class="m-doc-self">Xend</a>(</span><span class="m-doc-wrap">) -> <a href="dip-SampleIterator-T.html" class="m-doc">dip::SampleIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an <em>x</em>-value iterator to the end</dd>
<dt id="dip-Distribution-Xend-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Xend-C" class="m-doc-self">Xend</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-SampleIterator-T.html#dip-ConstSampleIterator-T" class="m-doc">dip::ConstSampleIterator</a> <span class="m-label m-flat m-success">noexcept</span></span>
</dt>
<dd>Returns an <em>x</em>-value iterator to the end</dd>
<dt id="dip-Distribution-Ybegin-dip-uint-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Ybegin-dip-uint-" class="m-doc-self">Ybegin</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) -> <a href="dip-SampleIterator-T.html" class="m-doc">dip::SampleIterator</a></span>
</dt>
<dd>Returns an <em>y</em>-value iterator to the beginning</dd>
<dt id="dip-Distribution-Ybegin-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Ybegin-dip-uint--C" class="m-doc-self">Ybegin</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) const -> <a href="dip-SampleIterator-T.html#dip-ConstSampleIterator-T" class="m-doc">dip::ConstSampleIterator</a></span>
</dt>
<dd>Returns an <em>y</em>-value iterator to the beginning</dd>
<dt id="dip-Distribution-Yend-dip-uint-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Yend-dip-uint-" class="m-doc-self">Yend</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) -> <a href="dip-SampleIterator-T.html" class="m-doc">dip::SampleIterator</a></span>
</dt>
<dd>Returns an <em>y</em>-value iterator to the end</dd>
<dt id="dip-Distribution-Yend-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Yend-dip-uint--C" class="m-doc-self">Yend</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) const -> <a href="dip-SampleIterator-T.html#dip-ConstSampleIterator-T" class="m-doc">dip::ConstSampleIterator</a></span>
</dt>
<dd>Returns an <em>y</em>-value iterator to the end</dd>
<dt id="dip-Distribution-X-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-X-C" class="m-doc-self">X</a>(</span><span class="m-doc-wrap">) const -> std::vector<dfloat></span>
</dt>
<dd>Copies the <em>x</em> values to a new array</dd>
<dt id="dip-Distribution-Y-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Y-dip-uint--C" class="m-doc-self">Y</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) const -> std::vector<dfloat></span>
</dt>
<dd>Copies the <em>y</em> values to a new array</dd>
<dt id="dip-Distribution-Sort">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Sort" class="m-doc-self">Sort</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Sorts the data in the distribution according to the <em>x</em> values.</dd>
<dt id="dip-Distribution-Cumulative">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Cumulative" class="m-doc-self">Cumulative</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Converts the distribution to a cumulative distribution, where each element is the sum of
all elements up to that element in the original distribution (i.e. <em>x</em> spacing is ignored).</dd>
<dt id="dip-Distribution-Sum-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Sum-dip-uint--C" class="m-doc-self">Sum</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Computes the sum of the <em>y</em> values.</dd>
<dt id="dip-Distribution-NormalizeSum">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-NormalizeSum" class="m-doc-self">NormalizeSum</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Normalizes the sum of the <em>y</em> values.</dd>
<dt id="dip-Distribution-Integrate">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Integrate" class="m-doc-self">Integrate</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Converts the distribution to a cumulative distribution, where each element is the integral of
the original distribution up to that element. Make sure the data are sorted (see <code>Sort</code>).</dd>
<dt id="dip-Distribution-Integral-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Integral-dip-uint--C" class="m-doc-self">Integral</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index = 0) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Computes the integral of the distribution. Make sure the data are sorted (see <code>Sort</code>).</dd>
<dt id="dip-Distribution-NormalizeIntegral">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-NormalizeIntegral" class="m-doc-self">NormalizeIntegral</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Normalizes the integral of the distribution values. Make sure the data are sorted (see <code>Sort</code>).</dd>
<dt id="dip-Distribution-Differentiate">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-Differentiate" class="m-doc-self">Differentiate</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Converts the cumulative distribution to a distribution, where each element is the derivative of
the original distribution at that element. Make sure the data are sorted (see <code>Sort</code>).</dd>
<dt id="dip-Distribution-MaximumLikelihood">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-MaximumLikelihood" class="m-doc-self">MaximumLikelihood</a>(</span><span class="m-doc-wrap">) -> <a href="dip-Distribution.html#dip-Distribution-Container" class="m-doc">dip::Distribution::Container</a></span>
</dt>
<dd>Computes the most likely <em>x</em> values. In essence, returns the <em>x</em> values which maximize
the corresponding <em>y</em> value.</dd>
<dt id="dip-Distribution-SetSampling-PixelSize-CL-dfloat--dfloat-">
<span class="m-doc-wrap-bumper">void <a href="#dip-Distribution-SetSampling-PixelSize-CL-dfloat--dfloat-" class="m-doc-self">SetSampling</a>(</span><span class="m-doc-wrap"><a href="dip-PixelSize.html" class="m-doc">dip::PixelSize</a> const& pixelSize = {},
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> offset = 0.0,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> scaling = 1.0)</span>
</dt>
<dd>Fills the values for the <em>x</em> axis, starting with <code>pixelSize[0].magnitude * offset</code>,
and linear increments of <code>pixelSize[0].magnitude * scaling</code>, if the <code>pixelSize</code> is isotropic and has
physical units. The <code>XUnits</code> are also set to the units of the isotropic <code>pixelSize</code>, or otherwise
to “px”.</dd>
</dl>
</section>
<section id="operator-members">
<h2>Operators</h2>
<dl class="m-doc">
<dt id="dip-Distribution-operator%5B%5D-dip-uint-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-operator%5B%5D-dip-uint-" class="m-doc-self">operator[]</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index) -> <a href="dip-Distribution-Sample.html" class="m-doc">dip::Distribution::Sample</a></span>
</dt>
<dd>Gets the <em>x</em> and <em>y</em> values at location <code>index</code></dd>
<dt id="dip-Distribution-operator%5B%5D-dip-uint--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-operator%5B%5D-dip-uint--C" class="m-doc-self">operator[]</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> index) const -> <a href="dip-Distribution-ConstSample.html" class="m-doc">dip::Distribution::ConstSample</a></span>
</dt>
<dd>Gets the <em>x</em> and <em>y</em> values at location <code>index</code></dd>
<dt id="dip-Distribution-operator%2B%3D-Distribution-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-operator%2B%3D-Distribution-CL" class="m-doc-self">operator+=</a>(</span><span class="m-doc-wrap"><a href="dip-Distribution.html" class="m-doc">dip::Distribution</a> const& other) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Adds two distributions. Their <em>x</em> values must match exactly.</dd>
<dt id="dip-Distribution-operator%2A%3D-dfloat-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-operator%2A%3D-dfloat-" class="m-doc-self">operator*=</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> scale) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Scales the distribution, multiplying each <em>y</em> value by <code>scale</code>.</dd>
<dt id="dip-Distribution-operator%2F%3D-dfloat-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Distribution-operator%2F%3D-dfloat-" class="m-doc-self">operator/=</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> scale) -> <a href="dip-Distribution.html" class="m-doc">dip::Distribution</a>&</span>
</dt>
<dd>Scales the distribution, dividing each <em>y</em> value by <code>scale</code>.</dd>
</dl>
</section>
<section id="related">
<h2>Related</h2>
<dl class="m-doc">
<dt id="dip-operator%3C%3C-std-ostream-L-Distribution-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-operator%3C%3C-std-ostream-L-Distribution-CL" class="m-doc-self">dip::<wbr />operator<<</a>(</span><span class="m-doc-wrap">std::ostream& os,
<a href="dip-Distribution.html" class="m-doc">dip::Distribution</a> const& distribution) -> std::ostream&</span>
</dt>
<dd>Writes the distribution to a stream</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-operator%3C%3C-std-ostream-L-Histogram-CL" class="m-doc">dip::<wbr />operator<<</a>(</span><span class="m-doc-wrap">std::ostream& os,
<a href="dip-Histogram.html" class="m-doc">dip::Histogram</a> const& histogram) -> std::ostream&</span>
</dt>
<dd>You can output a <a href="dip-Histogram.html"><code>dip::Histogram</code></a> to <code>std::cout</code> or any other stream. Some
information about the histogram is printed.</dd>
</dl>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-operator%3C%3C-std-ostream-L-Histogram-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">std::ostream&
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-operator%3C%3C-std-ostream-L-Histogram-CL" class="m-doc-self">dip::<wbr />operator<<</a>(</span><span class="m-doc-wrap">std::ostream& os,
<a href="dip-Histogram.html" class="m-doc">dip::Histogram</a> const& histogram)</span></span>
<div class="m-doc-include m-code m-inverted m-text-right"><span class="cp">#include</span> <a class="cpf" href="file--diplib--histogram-h.html">"diplib/histogram.h"</a></div>
</h3>
<p>You can output a <a href="dip-Histogram.html"><code>dip::Histogram</code></a> to <code>std::cout</code> or any other stream. Some
information about the histogram is printed.</p>
</div></section>
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