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  <div class="section" id="the-diagonaloperator-class">
<h1>The <code class="docutils literal"><span class="pre">DiagonalOperator</span></code> class – …<a class="headerlink" href="#the-diagonaloperator-class" title="Permalink to this headline"></a></h1>
<dl class="class">
<dt id="nifty.DiagonalOperator">
<em class="property">class </em><code class="descclassname">nifty.</code><code class="descname">DiagonalOperator</code><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">nifty.operators.endomorphic_operator.endomorphic_operator.EndomorphicOperator</span></code></p>
<p>NIFTY class for diagonal operators.</p>
<p>The NIFTY DiagonalOperator class is a subclass derived from the
EndomorphicOperator. It multiplies an input field pixel-wise with its
diagonal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>domain</strong> : tuple of DomainObjects, i.e. Spaces and FieldTypes</p>
<blockquote>
<div><p>The domain on which the Operator’s input Field lives.</p>
</div></blockquote>
<p><strong>diagonal</strong> : {scalar, list, array, Field, d2o-object}</p>
<blockquote>
<div><p>The diagonal entries of the operator.</p>
</div></blockquote>
<p><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Indicates whether the input for the diagonal is bare or not
(default: False).</p>
</div></blockquote>
<p><strong>copy</strong> : boolean</p>
<blockquote>
<div><p>Internal copy of the diagonal (default: True)</p>
</div></blockquote>
<p><strong>distribution_strategy</strong> : string</p>
<blockquote>
<div><p>setting the prober distribution_strategy of the
diagonal (default : None). In case diagonal is d2o-object or Field,
their distribution_strategy is used as a fallback.</p>
</div></blockquote>
<p><strong>default_spaces</strong> : tuple of ints <em>optional</em></p>
<blockquote class="last">
<div><p>Defines on which space(s) of a given field the Operator acts by
default (default: None)</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><code class="xref py py-obj docutils literal"><span class="pre">EndomorphicOperator</span></code></p>
</div>
<p class="rubric">Notes</p>
<p>The ambiguity of bare or non-bare diagonal entries is based on the choice
of a matrix representation of the operator in question. The naive choice
of absorbing the volume weights into the matrix leads to a matrix-vector
calculus with the non-bare entries which seems intuitive, though.
The choice of keeping matrix entries and volume weights separate
deals with the bare entries that allow for correct interpretation
of the matrix entries; e.g., as variance in case of an covariance operator.</p>
<p class="rubric">Examples</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">x_space</span> <span class="o">=</span> <span class="n">RGSpace</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">D</span> <span class="o">=</span> <span class="n">DiagonalOperator</span><span class="p">(</span><span class="n">x_space</span><span class="p">,</span> <span class="n">diagonal</span><span class="o">=</span><span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">f</span> <span class="o">=</span> <span class="n">Field</span><span class="p">(</span><span class="n">x_space</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="mf">2.</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">res</span> <span class="o">=</span> <span class="n">D</span><span class="o">.</span><span class="n">times</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">res</span><span class="o">.</span><span class="n">val</span>
<span class="go">&lt;distributed_data_object&gt;</span>
<span class="go">array([ 2.,  6.,  4.,  8.,  12.])</span>
</pre></div>
</div>
<p class="rubric">Attributes</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.domain" title="nifty.DiagonalOperator.domain"><code class="xref py py-obj docutils literal"><span class="pre">domain</span></code></a></td>
<td><em>domain</em> – tuple of DomainObjects, i.e. Spaces and FieldTypes</td>
</tr>
<tr class="row-even"><td><code class="xref py py-obj docutils literal"><span class="pre">target</span></code></td>
<td><em>target</em> – tuple of DomainObjects, i.e. Spaces and FieldTypes</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.unitary" title="nifty.DiagonalOperator.unitary"><code class="xref py py-obj docutils literal"><span class="pre">unitary</span></code></a></td>
<td><em>unitary</em> – boolean</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.DiagonalOperator.self_adjoint" title="nifty.DiagonalOperator.self_adjoint"><code class="xref py py-obj docutils literal"><span class="pre">self_adjoint</span></code></a></td>
<td>States whether the Operator is self_adjoint or not.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.distribution_strategy" title="nifty.DiagonalOperator.distribution_strategy"><code class="xref py py-obj docutils literal"><span class="pre">distribution_strategy</span></code></a></td>
<td><em>distribution_strategy</em></td>
</tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.determinant" title="nifty.DiagonalOperator.determinant"><code class="xref py py-obj docutils literal"><span class="pre">determinant</span></code></a>()</td>
<td>Returns the determinant of the operator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.DiagonalOperator.diagonal" title="nifty.DiagonalOperator.diagonal"><code class="xref py py-obj docutils literal"><span class="pre">diagonal</span></code></a>([bare,&nbsp;copy])</td>
<td>Returns the diagonal of the Operator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.inverse_determinant" title="nifty.DiagonalOperator.inverse_determinant"><code class="xref py py-obj docutils literal"><span class="pre">inverse_determinant</span></code></a>()</td>
<td>Returns the inverse-determinant of the operator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.DiagonalOperator.inverse_diagonal" title="nifty.DiagonalOperator.inverse_diagonal"><code class="xref py py-obj docutils literal"><span class="pre">inverse_diagonal</span></code></a>([bare])</td>
<td>Returns the inverse-diagonal of the operator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.inverse_trace" title="nifty.DiagonalOperator.inverse_trace"><code class="xref py py-obj docutils literal"><span class="pre">inverse_trace</span></code></a>([bare])</td>
<td>Returns the inverse-trace of the operator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.DiagonalOperator.log_determinant" title="nifty.DiagonalOperator.log_determinant"><code class="xref py py-obj docutils literal"><span class="pre">log_determinant</span></code></a>()</td>
<td>Returns the log-eterminant of the operator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.set_diagonal" title="nifty.DiagonalOperator.set_diagonal"><code class="xref py py-obj docutils literal"><span class="pre">set_diagonal</span></code></a>(diagonal[,&nbsp;bare,&nbsp;copy])</td>
<td>Sets the diagonal of the Operator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.DiagonalOperator.trace" title="nifty.DiagonalOperator.trace"><code class="xref py py-obj docutils literal"><span class="pre">trace</span></code></a>([bare])</td>
<td>Returns the trace the operator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.DiagonalOperator.trace_log" title="nifty.DiagonalOperator.trace_log"><code class="xref py py-obj docutils literal"><span class="pre">trace_log</span></code></a>()</td>
<td>Returns the trave-log of the operator.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="nifty.DiagonalOperator.determinant">
<code class="descname">determinant</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.determinant"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.determinant" title="Permalink to this definition"></a></dt>
<dd><p>Returns the determinant of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<p><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>the determinant of the Operator</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.diagonal">
<code class="descname">diagonal</code><span class="sig-paren">(</span><em>bare=False</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.diagonal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.diagonal" title="Permalink to this definition"></a></dt>
<dd><p>Returns the diagonal of the Operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Whether the returned Field values should be bare or not.</p>
</div></blockquote>
<p><strong>copy</strong> : boolean</p>
<blockquote>
<div><p>Whether the returned Field should be copied or not.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : Field</p>
<blockquote class="last">
<div><p>The diagonal of the Operator.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.inverse_determinant">
<code class="descname">inverse_determinant</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.inverse_determinant"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.inverse_determinant" title="Permalink to this definition"></a></dt>
<dd><p>Returns the inverse-determinant of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>the inverse-determinant of the Operator</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.inverse_diagonal">
<code class="descname">inverse_diagonal</code><span class="sig-paren">(</span><em>bare=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.inverse_diagonal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.inverse_diagonal" title="Permalink to this definition"></a></dt>
<dd><p>Returns the inverse-diagonal of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Whether the returned Field values should be bare or not.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : Field</p>
<blockquote class="last">
<div><p>The inverse of the diagonal of the Operator.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.inverse_trace">
<code class="descname">inverse_trace</code><span class="sig-paren">(</span><em>bare=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.inverse_trace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.inverse_trace" title="Permalink to this definition"></a></dt>
<dd><p>Returns the inverse-trace of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Whether the returned Field values should be bare or not.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>The inverse of the trace of the Operator.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.log_determinant">
<code class="descname">log_determinant</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.log_determinant"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.log_determinant" title="Permalink to this definition"></a></dt>
<dd><p>Returns the log-eterminant of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>the log-determinant of the Operator</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.set_diagonal">
<code class="descname">set_diagonal</code><span class="sig-paren">(</span><em>diagonal</em>, <em>bare=False</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.set_diagonal"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.set_diagonal" title="Permalink to this definition"></a></dt>
<dd><p>Sets the diagonal of the Operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>diagonal</strong> : {scalar, list, array, Field, d2o-object}</p>
<blockquote>
<div><p>The diagonal entries of the operator.</p>
</div></blockquote>
<p><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Indicates whether the input for the diagonal is bare or not
(default: False).</p>
</div></blockquote>
<p><strong>copy</strong> : boolean</p>
<blockquote class="last">
<div><p>Specifies if a copy of the input shall be made (default: True).</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.trace">
<code class="descname">trace</code><span class="sig-paren">(</span><em>bare=False</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.trace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.trace" title="Permalink to this definition"></a></dt>
<dd><p>Returns the trace the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>bare</strong> : boolean</p>
<blockquote>
<div><p>Whether the returned Field values should be bare or not.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>The trace of the Operator.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="method">
<dt id="nifty.DiagonalOperator.trace_log">
<code class="descname">trace_log</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/operators/diagonal_operator/diagonal_operator.html#DiagonalOperator.trace_log"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.DiagonalOperator.trace_log" title="Permalink to this definition"></a></dt>
<dd><p>Returns the trave-log of the operator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> : scalar</p>
<blockquote class="last">
<div><p>the trace of the logarithm of the Operator.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

<dl class="attribute">
<dt id="nifty.DiagonalOperator.distribution_strategy">
<code class="descname">distribution_strategy</code><a class="headerlink" href="#nifty.DiagonalOperator.distribution_strategy" title="Permalink to this definition"></a></dt>
<dd><p><em>distribution_strategy</em></p>
<dl class="docutils">
<dt>string</dt>
<dd>Defines the way how the diagonal operator is distributed
among the nodes. Available distribution_strategies are:
‘fftw’, ‘equal’ and ‘not’.</dd>
<dt>Notes :</dt>
<dd><a class="reference external" href="https://arxiv.org/abs/1606.05385">https://arxiv.org/abs/1606.05385</a></dd>
</dl>
</dd></dl>

<dl class="attribute">
<dt id="nifty.DiagonalOperator.domain">
<code class="descname">domain</code><a class="headerlink" href="#nifty.DiagonalOperator.domain" title="Permalink to this definition"></a></dt>
<dd><p><em>domain</em> – tuple of DomainObjects, i.e. Spaces and FieldTypes
The domain on which the Operator’s input Field lives.
Every Operator which inherits from the abstract LinearOperator
base class must have this attribute.</p>
</dd></dl>

<dl class="attribute">
<dt id="nifty.DiagonalOperator.self_adjoint">
<code class="descname">self_adjoint</code><a class="headerlink" href="#nifty.DiagonalOperator.self_adjoint" title="Permalink to this definition"></a></dt>
<dd><p>States whether the Operator is self_adjoint or not.</p>
</dd></dl>

<dl class="attribute">
<dt id="nifty.DiagonalOperator.unitary">
<code class="descname">unitary</code><a class="headerlink" href="#nifty.DiagonalOperator.unitary" title="Permalink to this definition"></a></dt>
<dd><p><em>unitary</em> – boolean
States whether the Operator is unitary or not.
Every Operator which inherits from the abstract LinearOperator
base class must have this attribute.</p>
</dd></dl>

</dd></dl>

</div>


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