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<div class="section" id="convolve-fft">
<h1>convolve_fft<a class="headerlink" href="#convolve-fft" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="astropy.nddata.convolution.convolve.convolve_fft">
<tt class="descclassname">astropy.nddata.convolution.convolve.</tt><tt class="descname">convolve_fft</tt><big>(</big><em>array</em>, <em>kernel</em>, <em>boundary='fill'</em>, <em>fill_value=0</em>, <em>crop=True</em>, <em>return_fft=False</em>, <em>fft_pad=True</em>, <em>psf_pad=False</em>, <em>interpolate_nan=False</em>, <em>quiet=False</em>, <em>ignore_edge_zeros=False</em>, <em>min_wt=0.0</em>, <em>normalize_kernel=False</em>, <em>fftn=<function fftn at 0x15787d0></em>, <em>ifftn=<function ifftn at 0x1578848></em>, <em>complex_dtype=<type 'complex'></em><big>)</big><a class="reference external" href="http://github.com/astropy/astropy/tree/v0.2.4/astropy/nddata/convolution/convolve.py#L167" title="Push the Edit button on the next page"><span class="edit-on-github viewcode-link"> [edit on github]</span></a><a class="reference internal" href="../_modules/astropy/nddata/convolution/convolve.html#convolve_fft"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#astropy.nddata.convolution.convolve.convolve_fft" title="Permalink to this definition">¶</a></dt>
<dd><p>Convolve an ndarray with an nd-kernel. Returns a convolved image with
shape = array.shape. Assumes kernel is centered.</p>
<p><a class="reference internal" href="#astropy.nddata.convolution.convolve.convolve_fft" title="astropy.nddata.convolution.convolve.convolve_fft"><tt class="xref py py-obj docutils literal"><span class="pre">convolve_fft</span></tt></a> differs from <tt class="xref py py-obj docutils literal"><span class="pre">scipy.signal.fftconvolve</span></tt> in a few ways:</p>
<ul class="simple">
<li>It can treat NaN’s as zeros or interpolate over them.</li>
<li><tt class="xref py py-obj docutils literal"><span class="pre">inf</span></tt> values are treated as <tt class="xref py py-obj docutils literal"><span class="pre">NaN</span></tt></li>
<li>(optionally) It pads to the nearest 2^n size to improve FFT speed.</li>
<li>Its only valid <tt class="xref py py-obj docutils literal"><span class="pre">mode</span></tt> is ‘same’ (i.e., the same shape array is returned)</li>
<li>It lets you use your own fft, e.g.,
<a class="reference external" href="http://pypi.python.org/pypi/pyFFTW">pyFFTW</a> or
<a class="reference external" href="http://pypi.python.org/pypi/PyFFTW3/0.2.1">pyFFTW3</a> , which can lead to
performance improvements, depending on your system configuration. pyFFTW3
is threaded, and therefore may yield significant performance benefits on
multi-core machines at the cost of greater memory requirements. Specify
the <tt class="xref py py-obj docutils literal"><span class="pre">fftn</span></tt> and <tt class="xref py py-obj docutils literal"><span class="pre">ifftn</span></tt> keywords to override the default, which is
<tt class="xref py py-obj docutils literal"><span class="pre">numpy.fft.fft</span></tt> and <tt class="xref py py-obj docutils literal"><span class="pre">numpy.fft.ifft</span></tt>.</li>
</ul>
<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>array</strong> : <tt class="xref py py-obj docutils literal"><span class="pre">numpy.ndarray</span></tt></p>
<blockquote>
<div><p>Array to be convolved with <tt class="xref py py-obj docutils literal"><span class="pre">kernel</span></tt></p>
</div></blockquote>
<p><strong>kernel</strong> : <tt class="xref py py-obj docutils literal"><span class="pre">numpy.ndarray</span></tt></p>
<blockquote>
<div><p>Will be normalized if <tt class="xref py py-obj docutils literal"><span class="pre">normalize_kernel</span></tt> is set. Assumed to be
centered (i.e., shifts may result if your kernel is asymmetric)</p>
</div></blockquote>
<p><strong>boundary</strong> : {‘fill’, ‘wrap’}</p>
<blockquote>
<div><p>A flag indicating how to handle boundaries:</p>
<blockquote>
<div><ul class="simple">
<li>‘fill’: set values outside the array boundary to fill_value
(default)</li>
<li>‘wrap’: periodic boundary</li>
</ul>
</div></blockquote>
</div></blockquote>
<p><strong>interpolate_nan</strong> : bool</p>
<blockquote>
<div><p>The convolution will be re-weighted assuming NAN values are meant to be
ignored, not treated as zero. If this is off, all NaN values will be
treated as zero.</p>
</div></blockquote>
<p><strong>ignore_edge_zeros</strong> : bool</p>
<blockquote>
<div><p>Ignore the zero-pad-created zeros. This will effectively decrease
the kernel area on the edges but will not re-normalize the kernel.
This parameter may result in ‘edge-brightening’ effects if you’re using
a normalized kernel</p>
</div></blockquote>
<p><strong>min_wt</strong> : float</p>
<blockquote>
<div><p>If ignoring NANs/zeros, force all grid points with a weight less than
this value to NAN (the weight of a grid point with <em>no</em> ignored
neighbors is 1.0).
If <tt class="xref py py-obj docutils literal"><span class="pre">min_wt</span></tt> == 0.0, then all zero-weight points will be set to zero
instead of NAN (which they would be otherwise, because 1/0 = nan).
See the examples below</p>
</div></blockquote>
<p><strong>normalize_kernel</strong> : function or boolean</p>
<blockquote>
<div><p>If specified, this is the function to divide kernel by to normalize it.
e.g., normalize_kernel=np.sum means that kernel will be modified to be:
kernel = kernel / np.sum(kernel). If True, defaults to
normalize_kernel = np.sum</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns :</th><td class="field-body"><p class="first"><strong>default</strong> : ndarray</p>
<blockquote>
<div><p><strong>array</strong> convolved with <tt class="xref py py-obj docutils literal"><span class="pre">kernel</span></tt>.
If <tt class="xref py py-obj docutils literal"><span class="pre">return_fft</span></tt> is set, returns fft(<strong>array</strong>) * fft(<tt class="xref py py-obj docutils literal"><span class="pre">kernel</span></tt>).
If crop is not set, returns the image, but with the fft-padded size
instead of the input size</p>
</div></blockquote>
</td>
</tr>
<tr class="field-odd field"><th class="field-name" colspan="2">Other Parameters:</th></tr>
<tr class="field-odd field"><td> </td><td class="field-body"><p class="first"><strong>fft_pad</strong> : bool</p>
<blockquote>
<div><p>Default on. Zero-pad image to the nearest 2^n</p>
</div></blockquote>
<p><strong>psf_pad</strong> : bool</p>
<blockquote>
<div><p>Default off. Zero-pad image to be at least the sum of the image sizes
(in order to avoid edge-wrapping when smoothing)</p>
</div></blockquote>
<p><strong>crop</strong> : bool</p>
<blockquote>
<div><p>Default on. Return an image of the size of the largest input image.
If the images are asymmetric in opposite directions, will return the
largest image in both directions.
For example, if an input image has shape [100,3] but a kernel with shape
[6,6] is used, the output will be [100,6].</p>
</div></blockquote>
<p><strong>return_fft</strong> : bool</p>
<blockquote>
<div><p>Return the fft(image)*fft(kernel) instead of the convolution (which is
ifft(fft(image)*fft(kernel))). Useful for making PSDs.</p>
</div></blockquote>
<p><strong>nthreads</strong> : int</p>
<blockquote>
<div><p>if fftw3 is installed, can specify the number of threads to allow FFTs
to use. Probably only helpful for large arrays</p>
</div></blockquote>
<p><strong>fftn, ifftn</strong> : functions</p>
<blockquote>
<div><p>The fft and inverse fft functions. Can be overridden to use your own
ffts, e.g. an fftw3 wrapper or scipy’s fftn, e.g.
<tt class="xref py py-obj docutils literal"><span class="pre">fftn=scipy.fftpack.fftn</span></tt></p>
</div></blockquote>
<p><strong>complex_dtype</strong> : np.complex</p>
<blockquote class="last">
<div><p>Which complex dtype to use. <tt class="xref py py-obj docutils literal"><span class="pre">numpy</span></tt> has a range of options, from 64 to
256.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition-see-also admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="astropy.nddata.convolution.convolve.convolve.html#astropy.nddata.convolution.convolve.convolve" title="astropy.nddata.convolution.convolve.convolve"><tt class="xref py py-obj docutils literal"><span class="pre">convolve</span></tt></a></dt>
<dd>Convolve is a non-fft version of this code.</dd>
</dl>
</div>
<p class="rubric">Examples</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="go">array([ 1., 4., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="go">array([ 1., 4., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="go">array([ 1., 0., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</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="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="go">array([ 1., 2., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">interpolate_nan</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="go">array([ 1., 0., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">interpolate_nan</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">min_wt</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">)</span>
<span class="go">array([ 1., nan, 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">interpolate_nan</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="go">array([ 1., 4., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">interpolate_nan</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">normalize_kernel</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">ignore_edge_zeros</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="go">array([ 1., 2., 3.])</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">scipy.fftpack</span> <span class="c"># optional - requires scipy</span>
<span class="gp">>>> </span><span class="n">convolve_fft</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">interpolate_nan</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">normalize_kernel</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">ignore_edge_zeros</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span>
<span class="gp">... </span> <span class="n">fftn</span><span class="o">=</span><span class="n">scipy</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">fft</span><span class="p">,</span> <span class="n">ifftn</span><span class="o">=</span><span class="n">scipy</span><span class="o">.</span><span class="n">fftpack</span><span class="o">.</span><span class="n">ifft</span><span class="p">)</span>
<span class="go">array([ 1., 2., 3.])</span>
</pre></div>
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