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<div class="bodywrapper"> <div class="body" id="spc-section-body"> <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"><=</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">>=</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> </div> </div> </div> </div> </div> </div> </div> <div class="container container-navbar-bottom"> <div class="spc-navbar"> </div> </div> <div class="container"> <div class="footer"> <div class="row-fluid"> <ul class="inline pull-left"> <li> © Copyright 2008-2016, The Scipy community. </li> <li> Last updated on Sep 21, 2017. </li> <li> Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 1.6.3. </li> </ul> </div> </div> </div> </body> </html>