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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<title>arrayfire.lapack module — ArrayFire Python documentation</title>
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<div class="section" id="module-arrayfire.lapack">
<span id="arrayfire-lapack-module"></span><h1>arrayfire.lapack module<a class="headerlink" href="#module-arrayfire.lapack" title="Permalink to this headline">¶</a></h1>
<p>Dense Linear Algebra functions (solve, inverse, etc).</p>
<dl class="function">
<dt id="arrayfire.lapack.cholesky">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">cholesky</code><span class="sig-paren">(</span><em>A</em>, <em>is_upper=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.cholesky" title="Permalink to this definition">¶</a></dt>
<dd><p>Cholesky decomposition</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional, symmetric, positive definite matrix.</p>
</div></blockquote>
<p><strong>is_upper: optional: bool. default: True</strong></p>
<blockquote>
<div><p>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">(R,info): tuple of af.Array, int.</p>
<blockquote class="last">
<div><ul class="simple">
<li>R - triangular matrix.</li>
<li>info - 0 if decomposition sucessful.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.cholesky_inplace">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">cholesky_inplace</code><span class="sig-paren">(</span><em>A</em>, <em>is_upper=True</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky_inplace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.cholesky_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place Cholesky decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>a 2 dimensional, symmetric, positive definite matrix.</li>
<li>Trinangular matrix on exit.</li>
</ul>
</div></blockquote>
<p><strong>is_upper: optional: bool. default: True.</strong></p>
<blockquote>
<div><p>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>info</strong> : int.</p>
<blockquote class="last">
<div><p>0 if decomposition sucessful.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.det">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">det</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#det"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.det" title="Permalink to this definition">¶</a></dt>
<dd><p>Determinant of a matrix.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>A 2 dimensional arrayfire array</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">res: scalar</p>
<blockquote class="last">
<div><ul class="simple">
<li>Determinant of the matrix.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.inverse">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">inverse</code><span class="sig-paren">(</span><em>A</em>, <em>options=<MATPROP.NONE: 0></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#inverse"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.inverse" title="Permalink to this definition">¶</a></dt>
<dd><p>Invert a matrix.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>A 2 dimensional arrayfire array</li>
</ul>
</div></blockquote>
<p><strong>options: optional: af.MATPROP. default: af.MATPROP.NONE.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Additional options to speed up computations.</li>
<li>Currently needs to be one of <cite>af.MATPROP.NONE</cite>.</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">AI: af.Array</p>
<blockquote class="last">
<div><ul class="simple">
<li>A 2 dimensional array that is the inverse of <cite>A</cite></li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.is_lapack_available">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">is_lapack_available</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#is_lapack_available"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.is_lapack_available" title="Permalink to this definition">¶</a></dt>
<dd><p>Function to check if the arrayfire library was built with lapack support.</p>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.lu">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">lu</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#lu"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.lu" title="Permalink to this definition">¶</a></dt>
<dd><p>LU decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional arrayfire array.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">(L,U,P): tuple of af.Arrays</p>
<blockquote class="last">
<div><ul class="simple">
<li>L - Lower triangular matrix.</li>
<li>U - Upper triangular matrix.</li>
<li>P - Permutation array.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.lu_inplace">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">lu_inplace</code><span class="sig-paren">(</span><em>A</em>, <em>pivot='lapack'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#lu_inplace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.lu_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place LU decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>a 2 dimensional arrayfire array on entry.</li>
<li>Contains L in the lower triangle on exit.</li>
<li>Contains U in the upper triangle on exit.</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">P: af.Array</p>
<blockquote class="last">
<div><ul class="simple">
<li>Permutation array.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.norm">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">norm</code><span class="sig-paren">(</span><em>A</em>, <em>norm_type=<NORM.VECTOR_2: 2></em>, <em>p=1.0</em>, <em>q=1.0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#norm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.norm" title="Permalink to this definition">¶</a></dt>
<dd><p>Norm of an array or a matrix.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>A 1 or 2 dimensional arrayfire array</li>
</ul>
</div></blockquote>
<p><strong>norm_type: optional: af.NORM. default: af.NORM.EUCLID.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Type of norm to be calculated.</li>
</ul>
</div></blockquote>
<p><strong>p: scalar. default 1.0.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Used only if <cite>norm_type</cite> is one of <cite>af.NORM.VECTOR_P</cite>, <cite>af.NORM_MATRIX_L_PQ</cite></li>
</ul>
</div></blockquote>
<p><strong>q: scalar. default 1.0.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Used only if <cite>norm_type</cite> is <cite>af.NORM_MATRIX_L_PQ</cite></li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">res: scalar</p>
<blockquote class="last">
<div><ul class="simple">
<li>norm of the input</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.qr">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">qr</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#qr"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.qr" title="Permalink to this definition">¶</a></dt>
<dd><p>QR decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional arrayfire array.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">(Q,R,T): tuple of af.Arrays</p>
<blockquote class="last">
<div><ul class="simple">
<li>Q - Orthogonal matrix.</li>
<li>R - Upper triangular matrix.</li>
<li>T - Vector containing additional information to solve a least squares problem.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.qr_inplace">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">qr_inplace</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#qr_inplace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.qr_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place QR decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>a 2 dimensional arrayfire array on entry.</li>
<li>Packed Q and R matrices on exit.</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">T: af.Array</p>
<blockquote class="last">
<div><ul class="simple">
<li>Vector containing additional information to solve a least squares problem.</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.rank">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">rank</code><span class="sig-paren">(</span><em>A</em>, <em>tol=1e-05</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#rank"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.rank" title="Permalink to this definition">¶</a></dt>
<dd><p>Rank of a matrix.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>A 2 dimensional arrayfire array</li>
</ul>
</div></blockquote>
<p><strong>tol: optional: scalar. default: 1E-5.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Tolerance for calculating rank</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">r: int</p>
<blockquote class="last">
<div><ul class="simple">
<li>Rank of <cite>A</cite> within the given tolerance</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.solve">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">solve</code><span class="sig-paren">(</span><em>A</em>, <em>B</em>, <em>options=<MATPROP.NONE: 0></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#solve"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.solve" title="Permalink to this definition">¶</a></dt>
<dd><p>Solve a system of linear equations.</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional arrayfire array representing the coefficients of the system.</p>
</div></blockquote>
<p><strong>B: af.Array</strong></p>
<blockquote>
<div><p>A 1 or 2 dimensional arrayfire array representing the constants of the system.</p>
</div></blockquote>
<p><strong>options: optional: af.MATPROP. default: af.MATPROP.NONE.</strong></p>
<blockquote>
<div><ul class="simple">
<li>Additional options to speed up computations.</li>
<li>Currently needs to be one of <cite>af.MATPROP.NONE</cite>, <cite>af.MATPROP.LOWER</cite>, <cite>af.MATPROP.UPPER</cite>.</li>
</ul>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">X: af.Array</p>
<blockquote class="last">
<div><p>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.solve_lu">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">solve_lu</code><span class="sig-paren">(</span><em>A</em>, <em>P</em>, <em>B</em>, <em>options=<MATPROP.NONE: 0></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#solve_lu"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.solve_lu" title="Permalink to this definition">¶</a></dt>
<dd><p>Solve a system of linear equations, using LU decomposition.</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>A: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>A 2 dimensional arrayfire array representing the coefficients of the system.</li>
<li>This matrix should be decomposed previously using <cite>lu_inplace(A)</cite>.</li>
</ul>
</div></blockquote>
<p><strong>P: af.Array</strong></p>
<blockquote>
<div><ul class="simple">
<li>Permutation array.</li>
<li>This array is the output of an earlier call to <cite>lu_inplace(A)</cite></li>
</ul>
</div></blockquote>
<p><strong>B: af.Array</strong></p>
<blockquote>
<div><p>A 1 or 2 dimensional arrayfire array representing the constants of the system.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">X: af.Array</p>
<blockquote class="last">
<div><p>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.svd">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">svd</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#svd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.svd" title="Permalink to this definition">¶</a></dt>
<dd><p>Singular Value Decomposition</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional arrayfire array.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">(U,S,Vt): tuple of af.Arrays</p>
<blockquote class="last">
<div><ul class="simple">
<li>U - A unitary matrix</li>
<li>S - An array containing the elements of diagonal matrix</li>
<li>Vt - A unitary matrix</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="arrayfire.lapack.svd_inplace">
<code class="descclassname">arrayfire.lapack.</code><code class="descname">svd_inplace</code><span class="sig-paren">(</span><em>A</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#svd_inplace"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#arrayfire.lapack.svd_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>Singular Value Decomposition</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>A: af.Array</strong></p>
<blockquote>
<div><p>A 2 dimensional arrayfire array.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">(U,S,Vt): tuple of af.Arrays</p>
<blockquote class="last">
<div><ul class="simple">
<li>U - A unitary matrix</li>
<li>S - An array containing the elements of diagonal matrix</li>
<li>Vt - A unitary matrix</li>
</ul>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
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