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  <div class="section" id="scipy-linalg-cholesky-banded">
<h1>scipy.linalg.cholesky_banded<a class="headerlink" href="#scipy-linalg-cholesky-banded" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="scipy.linalg.cholesky_banded">
<code class="descclassname">scipy.linalg.</code><code class="descname">cholesky_banded</code><span class="sig-paren">(</span><em>ab</em>, <em>overwrite_ab=False</em>, <em>lower=False</em>, <em>check_finite=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scipy/scipy/blob/4e64658/scipy/linalg/decomp_cholesky.py#L194-L247"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#scipy.linalg.cholesky_banded" title="Permalink to this definition">¶</a></dt>
<dd><p>Cholesky decompose a banded Hermitian positive-definite matrix</p>
<p>The matrix a is stored in ab either in lower diagonal or upper
diagonal ordered form:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">ab</span><span class="p">[</span><span class="n">u</span> <span class="o">+</span> <span class="n">i</span> <span class="o">-</span> <span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span>        <span class="p">(</span><span class="k">if</span> <span class="n">upper</span> <span class="n">form</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">)</span>
<span class="n">ab</span><span class="p">[</span>    <span class="n">i</span> <span class="o">-</span> <span class="n">j</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">==</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">]</span>        <span class="p">(</span><span class="k">if</span> <span class="n">lower</span> <span class="n">form</span><span class="p">;</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="n">j</span><span class="p">)</span>
</pre></div>
</div>
<p>Example of ab (shape of a is (6,6), u=2):</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">upper</span> <span class="n">form</span><span class="p">:</span>
<span class="o">*</span>   <span class="o">*</span>   <span class="n">a02</span> <span class="n">a13</span> <span class="n">a24</span> <span class="n">a35</span>
<span class="o">*</span>   <span class="n">a01</span> <span class="n">a12</span> <span class="n">a23</span> <span class="n">a34</span> <span class="n">a45</span>
<span class="n">a00</span> <span class="n">a11</span> <span class="n">a22</span> <span class="n">a33</span> <span class="n">a44</span> <span class="n">a55</span>

<span class="n">lower</span> <span class="n">form</span><span class="p">:</span>
<span class="n">a00</span> <span class="n">a11</span> <span class="n">a22</span> <span class="n">a33</span> <span class="n">a44</span> <span class="n">a55</span>
<span class="n">a10</span> <span class="n">a21</span> <span class="n">a32</span> <span class="n">a43</span> <span class="n">a54</span> <span class="o">*</span>
<span class="n">a20</span> <span class="n">a31</span> <span class="n">a42</span> <span class="n">a53</span> <span class="o">*</span>   <span class="o">*</span>
</pre></div>
</div>
<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>ab</strong> : (u + 1, M) array_like</p>
<blockquote>
<div><p>Banded matrix</p>
</div></blockquote>
<p><strong>overwrite_ab</strong> : bool, optional</p>
<blockquote>
<div><p>Discard data in ab (may enhance performance)</p>
</div></blockquote>
<p><strong>lower</strong> : bool, optional</p>
<blockquote>
<div><p>Is the matrix in the lower form. (Default is upper form)</p>
</div></blockquote>
<p><strong>check_finite</strong> : bool, optional</p>
<blockquote>
<div><p>Whether to check that the input matrix contains only finite numbers.
Disabling may give a performance gain, but may result in problems
(crashes, non-termination) if the inputs do contain infinities or NaNs.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>c</strong> : (u + 1, M) ndarray</p>
<blockquote class="last">
<div><p>Cholesky factorization of a, in the same banded format as ab</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>

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