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<span class="target" id="module-src._helper"></span><span class="target" id="module-src._helper.helper"></span><div class="section" id="helper-functions">
<h1>Helper functions<a class="headerlink" href="#helper-functions" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="src._helper.helper.block_outer_prod">
<code class="descclassname">src._helper.helper.</code><code class="descname">block_outer_prod</code><span class="sig-paren">(</span><em>x1</em>, <em>x2</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.block_outer_prod" title="Permalink to this definition">¶</a></dt>
<dd><p>multiply the amplitudes along different axes</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.block_outer_sum">
<code class="descclassname">src._helper.helper.</code><code class="descname">block_outer_sum</code><span class="sig-paren">(</span><em>x1</em>, <em>x2</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.block_outer_sum" title="Permalink to this definition">¶</a></dt>
<dd><p>update the new index after adding a new axis</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.crop_slice_ind">
<code class="descclassname">src._helper.helper.</code><code class="descname">crop_slice_ind</code><span class="sig-paren">(</span><em>Nd</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.crop_slice_ind" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the "slice" of Nd size.
In Python language, "slice" means the index of a matrix.
Slice can provide a smaller "view" of a larger matrix.</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.kaiser_bessel_ft">
<code class="descclassname">src._helper.helper.</code><code class="descname">kaiser_bessel_ft</code><span class="sig-paren">(</span><em>u</em>, <em>J</em>, <em>alpha</em>, <em>kb_m</em>, <em>d</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.kaiser_bessel_ft" title="Permalink to this definition">¶</a></dt>
<dd><p>interpolation weight for given J/alpha/kb-m</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.nufft_T">
<code class="descclassname">src._helper.helper.</code><code class="descname">nufft_T</code><span class="sig-paren">(</span><em>N</em>, <em>J</em>, <em>K</em>, <em>alpha</em>, <em>beta</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.nufft_T" title="Permalink to this definition">¶</a></dt>
<dd><p>equation (29) and (26)Fessler's paper
create the overlapping matrix CSSC (diagonal dominent matrix)
of J points
and then find out the pseudo-inverse of CSSC</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.nufft_alpha_kb_fit">
<code class="descclassname">src._helper.helper.</code><code class="descname">nufft_alpha_kb_fit</code><span class="sig-paren">(</span><em>N</em>, <em>J</em>, <em>K</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.nufft_alpha_kb_fit" title="Permalink to this definition">¶</a></dt>
<dd><p>find out parameters alpha and beta
of scaling factor st['sn']
Note, when J = 1 , alpha is hardwired as [1,0,0...]
(uniform scaling factor)</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.nufft_offset">
<code class="descclassname">src._helper.helper.</code><code class="descname">nufft_offset</code><span class="sig-paren">(</span><em>om</em>, <em>J</em>, <em>K</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.nufft_offset" title="Permalink to this definition">¶</a></dt>
<dd><p>For every om points(outside regular grids), find the nearest
central grid (from Kd dimension)</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.nufft_r">
<code class="descclassname">src._helper.helper.</code><code class="descname">nufft_r</code><span class="sig-paren">(</span><em>om</em>, <em>N</em>, <em>J</em>, <em>K</em>, <em>alpha</em>, <em>beta</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.nufft_r" title="Permalink to this definition">¶</a></dt>
<dd><p>equation (30) of Fessler's paper</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.nufft_scale1">
<code class="descclassname">src._helper.helper.</code><code class="descname">nufft_scale1</code><span class="sig-paren">(</span><em>N</em>, <em>K</em>, <em>alpha</em>, <em>beta</em>, <em>Nmid</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.nufft_scale1" title="Permalink to this definition">¶</a></dt>
<dd><p>calculate image space scaling factor</p>
</dd></dl>
<dl class="function">
<dt id="src._helper.helper.preindex_copy">
<code class="descclassname">src._helper.helper.</code><code class="descname">preindex_copy</code><span class="sig-paren">(</span><em>Nd</em>, <em>Kd</em><span class="sig-paren">)</span><a class="headerlink" href="#src._helper.helper.preindex_copy" title="Permalink to this definition">¶</a></dt>
<dd><p>Building the array index for copying two arrays of sizes Nd and Kd</p>
<p>The output array2 is either truncated (if Nd > Kd) or zero-padded (if Nd < Kd)</p>
<dl class="docutils">
<dt>input: Nd: tuple, the dimensions of array1</dt>
<dd>Kd: tuple, the dimensions of array2</dd>
<dt>output: inlist: the index of the input array1</dt>
<dd>outlist: the index of the output array2
nelem: the product of all the smaller lengths along each dimension</dd>
</dl>
<p>example:</p>
</dd></dl>
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