Commit c40c8571 authored by Philipp Frank's avatar Philipp Frank
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added html and docktree files

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,12],procedur:2,process:18,product:[0,6,11],program:11,project:[20,21],projection_field:21,projectionoper:[0,18,27],propag:22,propagatoroper:[0,12,18,27],proper:5,properli:18,properti:[18,28],prototyp:11,provid:[1,5,6,12,16,17,18,23,29],pundex:20,pure:6,pyfftw:[6,17],pyhealpix:[5,7],python:11,quantiti:28,question:3,quotat:11,rais:[0,2,5,7,9,13,18,20,21,22,23,24,27,28],random:6,random_typ:6,rapidli:11,reach:[1,2],real:[6,7,9,11,13,20,24,28],real_pow:6,real_sign:6,realiz:6,reason:[8,10,11,14,15,26],reduc:28,refer:[1,7,9,13,14,15,20,24],regardless:11,regular:[11,28],reineck:[7,9,13,14],relat:5,relev:28,reli:5,replac:28,repres:[7,9,13,20,24,28],represent:[3,6,11,13,17],requir:28,res:[3,21],reset_count:1,resolut:[7,9,11,13,15,28],respect:[5,7,9,13,20,22,24,28],respons:22,responseoper:[0,18],restart:1,result:[6,20],retrun:6,revisit:[7,9,13,14],rg_space:26,rgrgtransform:[0,22,29],rgspace:[0,3,5,6,17,21,22,23,26,27,28],rho:20,ring:7,routin:18,same:[6,13,18],satisfactorili:5,scalar:[2,3,6,17],scale:[7,9,13,20,24,28],scheme:[1,2],scientif:22,search:11,second:[1,13,24,28],see:[0,6,17],seem:3,select:5,self:6,self_adjoint:[3,21,22,27],selig:11,seljebotn:[7,9,13,14],sensibl:5,separ:[2,3,6],set:[3,6,11,13,18,20,23,24,27],set_diagon:3,set_val:6,sever:18,shall:[3,6,7,9,13,20,24,28],shape:[6,7,9,13,17,20,24],shift:26,should:[3,5,6,17,20,26],sigma:[7,9,13,20,23,24,27,28],signal:[6,11,18,22],sinc:5,singl:5,situ:[1,2],situat:5,size:2,slicing_transform:[8,10,14,15],slicingtransform:[8,10,14,15],smooth:[7,9,13,20,23,24,27,28],smoothingoper:[0,18],softwar:5,solv:1,some:[18,28],sort:20,sourc:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,20,21,22,23,24,26,27,28],space:[0,3,5,6,7,8,9,10,11,13,14,15,17,18,20,21,22,23,24,26,27],spatial:[11,28],spec:22,specfi:6,specif:[6,18,28],specifi:[1,2,3,5,6,7,9,13,17,18,20,24,28],spectra:[6,17,20],spectrum:[6,20],speed:22,spepar:24,sphere:[5,13,14,15,28],spheric:[7,9,11,14,28],split:18,springer:1,squar:5,standard:[6,7,9,13,20,24,28],state:[0,3,5,18,21,22,23,27],std:6,step:[1,2],stop:2,stopiter:2,store:[6,17,18,28],str:[7,9,13,20,24,28],strategi:[6,17,20],string:[3,5,6,17],structur:28,subclass:[3,7,9,13,18,24,28],subspac:6,sum:[7,9,13,20,24,28],suppli:[1,2],support:[6,17],sverr:[7,9,13,14],symmetr:24,symmetri:28,synthes:[6,13,24,28],synthet:6,system:[1,28],take:[6,7,9,13,18,20,24,26,28],taken:11,target:[0,5,18,23],target_dtyp:[0,5],than:[7,9,13,20,24,27,28],thei:[7,9,11,13,20,24,28],them:[6,17],thereaft:28,therebi:11,therefor:[6,18],thi:[0,1,2,3,5,6,7,9,11,12,13,17,18,20,21,22,23,24,27,28],thoma:1,those:[11,18],though:3,thu:11,time:[0,1,2,3,5,12,18,21,23,27],titl:28,todo:28,togeth:[7,9,13,20,24,28],toler:[1,2],too:24,toolkit:11,top:[7,9,13,20,24],total:[6,7,9,13,20,24,28],total_volum:[6,7,9,13,20,24,28],trace:[3,18],trace_log:3,transform:[0,1,5,6,7,8,9,10,13,14,15,18,26,28],translat:22,trave:3,treat:6,tri:[6,17],tupl:[0,3,5,6,7,9,13,17,18,20,21,22,23,24,26,27,28],two:[0,7,9,13,14,15,24,28],type:[5,6,17,18,28],typeerror:[0,21,28],typic:23,umer:11,underli:[6,7,9,11,13,20,24,28],undershot:[1,2],uniform:[6,17],uniqu:[5,18,28],unitari:[0,3,5,18,21,22,23,27],unstructur:[6,17],use:6,used:[2,3,6,7,9,13,17,20,24,28],useful:0,user:[1,2,5,11,23,28],uses:[6,17],using:18,val:[3,6,13,17,21,22,23,24,26,27,28],valu:[3,6,7,9,13,17,20,24,26,28],valueerror:[5,7,9,13,22,23,27],variabl:1,varianc:3,vector:[3,20,24],veri:[0,18],verlag:1,versatil:11,version:[6,7,9,13,20,24],via:27,vol:11,volum:[3,6,7,9,13,20,24,28],wai:3,weight:[3,6,7,9,13,20,24],welcom:11,well:[18,28],what:[13,24,28],when:[1,2],whenev:5,where:[5,20,24],whether:[0,3,5,6,18,21,22,23,24,26,27],which:[0,1,2,3,5,6,7,8,9,10,11,13,14,15,17,18,20,21,22,23,24,26,27,28],whole:[6,17],wiener:22,wihtin:18,wise:3,within:[5,11],without:11,work:[5,6,17],world:11,would:18,write:28,written:11,x_space:[3,21,22],york:1,zero:[7,9,13,20,24,28],zerocent:[5,24,26]},titles:["The <code class=\"docutils literal\"><span class=\"pre\">ComposedOperator</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">ConjugateGradient</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">DescentMinimizer</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">DiagonalOperator</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">EndomorphicOperator</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">FFTOperator</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">Field</span></code> class \u2013 \u2026","The <code class=\"docutils literal\"><span class=\"pre\">GLSpace</span></code> class \u2013 Gauss-Legendre pixelization of the sphere","The <code class=\"docutils literal\"><span class=\"pre\">GLLMTransformation</span></code> class \u2013 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<div class="section" id="the-smoothingoperator-class">
<h1>The <code class="docutils literal"><span class="pre">SmoothingOperator</span></code> class – …<a class="headerlink" href="#the-smoothingoperator-class" title="Permalink to this headline"></a></h1>
<dl class="class">
<dt id="nifty.SmoothingOperator">
<em class="property">class </em><code class="descclassname">nifty.</code><code class="descname">SmoothingOperator</code><a class="reference internal" href="_modules/nifty/operators/smoothing_operator/smoothing_operator.html#SmoothingOperator"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.SmoothingOperator" 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 smoothing operators.</p>
<p>The NIFTy SmoothingOperator smooths Fields, with a given kernel length.
Fields which are not living over a PowerSpace are smoothed
via a gaussian convolution. Fields living over the PowerSpace are directly
smoothed.</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> : DomainObject, i.e. Space or FieldType</p>
<blockquote>
<div><p>The Space on which the operator acts. The SmoothingOperator
can only live on one space or FieldType</p>
</div></blockquote>
<p><strong>sigma</strong> : float</p>
<blockquote>
<div><p>Sets the length of the Gaussian convolution kernel</p>
</div></blockquote>
<p><strong>log_distances</strong> : boolean</p>
<blockquote>
<div><p>States whether the convolution happens on the logarithmic grid or not.</p>
</div></blockquote>
<p><strong>default_spaces</strong> : tuple of ints <em>optional</em></p>
<blockquote>
<div><p>Defines on which space(s) of a given field the Operator acts by
default (default: None)</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Raises:</th><td class="field-body"><p class="first"><strong>ValueError</strong></p>
<blockquote class="last">
<div><dl class="docutils">
<dt>Raised if</dt>
<dd><ul class="first last simple">
<li>the given domain inherits more than one space. The
SmoothingOperator acts only on one Space.</li>
</ul>
</dd>
</dl>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="diagonal_operator.html#nifty.DiagonalOperator" title="nifty.DiagonalOperator"><code class="xref py py-obj docutils literal"><span class="pre">DiagonalOperator</span></code></a>, <a class="reference internal" href="#nifty.SmoothingOperator" title="nifty.SmoothingOperator"><code class="xref py py-obj docutils literal"><span class="pre">SmoothingOperator</span></code></a>, <a class="reference internal" href="propagator_operator.html#nifty.PropagatorOperator" title="nifty.PropagatorOperator"><code class="xref py py-obj docutils literal"><span class="pre">PropagatorOperator</span></code></a>, <a class="reference internal" href="projection_operator.html#nifty.ProjectionOperator" title="nifty.ProjectionOperator"><code class="xref py py-obj docutils literal"><span class="pre">ProjectionOperator</span></code></a>, <a class="reference internal" href="composed_operator.html#nifty.ComposedOperator" title="nifty.ComposedOperator"><code class="xref py py-obj docutils literal"><span class="pre">ComposedOperator</span></code></a></p>
</div>
<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</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">S</span> <span class="o">=</span> <span class="n">SmoothingOperator</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="mf">1.</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</span><span class="p">,</span> <span class="n">val</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">S</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="o">.</span><span class="n">val</span>
<span class="go">&lt;distributed_data_object&gt;</span>
<span class="go">array([ 3., 3., 3., 3., 3.])</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.SmoothingOperator.domain" title="nifty.SmoothingOperator.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.SmoothingOperator.unitary" title="nifty.SmoothingOperator.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.SmoothingOperator.self_adjoint" title="nifty.SmoothingOperator.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>
</tbody>
</table>
<table border="1" class="docutils">
<colgroup>
<col width="14%" />
<col width="86%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>sigma</td>
<td>(float) Sets the length of the Gaussian convolution kernel</td>
</tr>
<tr class="row-even"><td>log_distances</td>
<td>(boolean) States whether the convolution happens on the logarithmic grid or not.</td>
</tr>
</tbody>
</table>
<dl class="attribute">
<dt id="nifty.SmoothingOperator.domain">
<code class="descname">domain</code><a class="headerlink" href="#nifty.SmoothingOperator.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.SmoothingOperator.self_adjoint">
<code class="descname">self_adjoint</code><a class="headerlink" href="#nifty.SmoothingOperator.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.SmoothingOperator.unitary">
<code class="descname">unitary</code><a class="headerlink" href="#nifty.SmoothingOperator.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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<div class="section" id="spaces">
<h1>Spaces<a class="headerlink" href="#spaces" title="Permalink to this headline"></a></h1>
<p>The <code class="xref py py-class docutils literal"><span class="pre">Space</span></code> classes of NIFTY represent geometrical spaces approximated by grids in the computer environment. Each subclass of the base class corresponds to a specific grid type and replaces some of the inherited methods with its own methods that are unique to the respective grid. This framework ensures an abstract handling of spaces independent of the underlying geometrical grid and the grid’s resolution.</p>
<p>Each instance of a <code class="xref py py-class docutils literal"><span class="pre">Space</span></code> needs to capture all structural and dimensional specifics of the grid and all computationally relevant quantities such as the data type of associated field values. These parameters are stored as properties of an instance of the class at its initialization, and they do not need to be accessed explicitly by the user thereafter. This prevents the writing of grid or resolution dependent code.</p>
<p>Spatial symmetries of a system can be exploited by corresponding coordinate transformations. Often, transformations from one basis to its harmonic counterpart can greatly reduce the computational complexity of algorithms. The harmonic basis is defined by the eigenbasis of the Laplace operator; e.g., for a flat position space it is the Fourier basis. This conjugation of bases is implemented in NIFTY by distinguishing conjugate space classes, which can be obtained by the instance method <em>get_codomain</em> (and checked for by <em>check_codomain</em>). Moreover, transformations between conjugate spaces are performed automatically if required.</p>
<div class="section" id="space-classes">
<h2>Space classes<a class="headerlink" href="#space-classes" title="Permalink to this headline"></a></h2>
<p>Next to the generic <code class="xref py py-class docutils literal"><span class="pre">Space</span></code> class, NIFTY has implementations of five subclasses, representing specific geometrical spaces and their discretizations.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="rg_space.html">The <code class="docutils literal"><span class="pre">RGSpace</span></code> class – Regular Cartesian grids</a></li>
<li class="toctree-l1"><a class="reference internal" href="hp_space.html">The <code class="docutils literal"><span class="pre">HPSpace</span></code> class – HEALPix discretization of the sphere</a></li>
<li class="toctree-l1"><a class="reference internal" href="gl_space.html">The <code class="docutils literal"><span class="pre">GLSpace</span></code> class – Gauss-Legendre pixelization of the sphere</a></li>
<li class="toctree-l1"><a class="reference internal" href="lm_space.html">The <code class="docutils literal"><span class="pre">LMSpace</span></code> class – Spherical Harmonics components</a></li>
<li class="toctree-l1"><a class="reference internal" href="power_space.html">The <code class="docutils literal"><span class="pre">PowerSpace</span></code> class – TODO: Title For PowerSpace</a></li>
<li class="toctree-l1"><a class="reference internal" href="power_indices.html">The <code class="docutils literal"><span class="pre">PowerIndices</span></code> class – TODO: Title For PowerIndices</a></li>
</ul>
</div>
</div>
<div class="section" id="the-space-class-the-base-space-object">
<h2>The <code class="docutils literal"><span class="pre">Space</span></code> class – The base Space object<a class="headerlink" href="#the-space-class-the-base-space-object" title="Permalink to this headline"></a></h2>
<dl class="class">
<dt id="nifty.Space">
<em class="property">class </em><code class="descclassname">nifty.</code><code class="descname">Space</code><a class="reference internal" href="_modules/nifty/spaces/space/space.html#Space"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.Space" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">nifty.domain_object.DomainObject</span></code></p>
<p>The abstract base class for all NIFTy spaces.</p>
<p>An instance of a space contains information about the manifolds
geometry and enhances the functionality of DomainObject by methods that
are needed for powerspectrum analysis and smoothing.</p>
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>None</strong></p>
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<tr class="field-even field"><th class="field-name">Raises:</th><td class="field-body"><p class="first"><strong>TypeError</strong></p>
<blockquote class="last">
<div><p>Raised if instantiated directly.</p>
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<p class="rubric">Notes</p>
<p><cite>Space</cite> is an abstract base class. In order to allow for instantiation
the methods <cite>get_distance_array</cite>, <cite>total_volume</cite> and <cite>copy</cite> must be
implemented as well as the abstract methods inherited from
<cite>DomainObject</cite>.</p>
<p class="rubric">Attributes</p>
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<tr class="row-odd"><td><code class="xref py py-obj docutils literal"><span class="pre">dim</span></code></td>
<td>Returns the number of pixel-dimensions the object has.</td>
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<tr class="row-even"><td><a class="reference internal" href="#nifty.Space.harmonic" title="nifty.Space.harmonic"><code class="xref py py-obj docutils literal"><span class="pre">harmonic</span></code></a></td>
<td>Returns True if this space is a harmonic space.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#nifty.Space.total_volume" title="nifty.Space.total_volume"><code class="xref py py-obj docutils literal"><span class="pre">total_volume</span></code></a></td>
<td>Returns the total volume of the space.</td>
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<tr class="row-even"><td><code class="xref py py-obj docutils literal"><span class="pre">shape</span></code></td>
<td>The domain-object’s shape contribution to the underlying array.</td>
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<p class="rubric">Methods</p>
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<tr class="row-odd"><td><a class="reference internal" href="#nifty.Space.copy" title="nifty.Space.copy"><code class="xref py py-obj docutils literal"><span class="pre">copy</span></code></a>()</td>
<td>Returns a copy of this Space instance.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#nifty.Space.get_distance_array" title="nifty.Space.get_distance_array"><code class="xref py py-obj docutils literal"><span class="pre">get_distance_array</span></code></a>(distribution_strategy)</td>
<td>The distances of the pixel to zero.</td>
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<tr class="row-odd"><td><a class="reference internal" href="#nifty.Space.get_fft_smoothing_kernel_function" title="nifty.Space.get_fft_smoothing_kernel_function"><code class="xref py py-obj docutils literal"><span class="pre">get_fft_smoothing_kernel_function</span></code></a>(sigma)</td>
<td>This method returns a smoothing kernel function.</td>
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<tr class="row-even"><td><a class="reference internal" href="#nifty.Space.hermitian_decomposition" title="nifty.Space.hermitian_decomposition"><code class="xref py py-obj docutils literal"><span class="pre">hermitian_decomposition</span></code></a>(x,&nbsp;axes[,&nbsp;…])</td>
<td>Decomposes x into its hermitian and anti-hermitian constituents.</td>
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<dl class="method">
<dt id="nifty.Space.copy">
<code class="descname">copy</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/spaces/space/space.html#Space.copy"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.Space.copy" title="Permalink to this definition"></a></dt>
<dd><p>Returns a copy of this Space instance.</p>
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<div><p>A copy of this instance.</p>
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</dd></dl>
<dl class="method">
<dt id="nifty.Space.get_distance_array">
<code class="descname">get_distance_array</code><span class="sig-paren">(</span><em>distribution_strategy</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/spaces/space/space.html#Space.get_distance_array"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.Space.get_distance_array" title="Permalink to this definition"></a></dt>
<dd><p>The distances of the pixel to zero.</p>
<p>This returns an array that gives for each pixel its distance to the
center of the manifolds grid.</p>
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>distribution_strategy</strong> : str</p>
<blockquote>
<div><p>The distribution_strategy which shall be used the returned
distributed_data_object.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">distributed_data_object</p>
<blockquote>
<div><p>A d2o containing the distances</p>
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<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><p class="first"><strong>NotImplementedError</strong></p>
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<div><p>If called for this abstract class.</p>
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</dd></dl>
<dl class="method">
<dt id="nifty.Space.get_fft_smoothing_kernel_function">
<code class="descname">get_fft_smoothing_kernel_function</code><span class="sig-paren">(</span><em>sigma</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/nifty/spaces/space/space.html#Space.get_fft_smoothing_kernel_function"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#nifty.Space.get_fft_smoothing_kernel_function" title="Permalink to this definition"></a></dt>
<dd><p>This method returns a smoothing kernel function.</p>
<p>This method, which is only implemented for harmonic spaces, helps
smoothing fields that live in a position space that has this space as
its harmonic space. The returned function multiplies field values of a
field with a zero centered Gaussian which corresponds to a convolution
with a Gaussian kernel and sigma standard deviation in position space.</p>
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<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>sigma</strong> : float</p>
<blockquote>
<div><p>A real number representing a physical scale on which the smoothing
takes place. The smoothing is defined with respect to the real
physical field and points that are closer together than one sigma
are blurred together. Mathematically sigma is the standard
deviation of a convolution with a normalized, zero-centered
Gaussian that takes place in position space.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">function (array-like -&gt; array-like)</p>
<blockquote>