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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="py function">
<dt id="arrayfire.lapack.cholesky">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">cholesky</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">is_upper</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.cholesky" title="Permalink to this definition">¶</a></dt>
<dd><p>Cholesky decomposition</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional, symmetric, positive definite matrix.</p>
</dd>
<dt><strong>is_upper: optional: bool. default: True</strong></dt><dd><p>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>(R,info): tuple of af.Array, int.</dt><dd><ul class="simple">
<li><p>R - triangular matrix.</p></li>
<li><p>info - 0 if decomposition sucessful.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.cholesky_inplace">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">cholesky_inplace</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">is_upper</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky_inplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.cholesky_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place Cholesky decomposition.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>a 2 dimensional, symmetric, positive definite matrix.</p></li>
<li><p>Trinangular matrix on exit.</p></li>
</ul>
</dd>
<dt><strong>is_upper: optional: bool. default: True.</strong></dt><dd><p>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>info</strong><span class="classifier">int.</span></dt><dd><p>0 if decomposition sucessful.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.det">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">det</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#det"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.det" title="Permalink to this definition">¶</a></dt>
<dd><p>Determinant of a matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 2 dimensional arrayfire array</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>res: scalar</dt><dd><ul class="simple">
<li><p>Determinant of the matrix.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.inverse">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">inverse</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">A</span></em>, <em class="sig-param"><span class="pre">options=<MATPROP.NONE:</span> <span class="pre">0></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#inverse"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.inverse" title="Permalink to this definition">¶</a></dt>
<dd><p>Invert a matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 2 dimensional arrayfire array</p></li>
</ul>
</dd>
<dt><strong>options: optional: af.MATPROP. default: af.MATPROP.NONE.</strong></dt><dd><ul class="simple">
<li><p>Additional options to speed up computations.</p></li>
<li><p>Currently needs to be one of <cite>af.MATPROP.NONE</cite>.</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>AI: af.Array</dt><dd><ul class="simple">
<li><p>A 2 dimensional array that is the inverse of <cite>A</cite></p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.is_lapack_available">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">is_lapack_available</span></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"><span class="pre">[source]</span></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="py function">
<dt id="arrayfire.lapack.lu">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">lu</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#lu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.lu" title="Permalink to this definition">¶</a></dt>
<dd><p>LU decomposition.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional arrayfire array.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>(L,U,P): tuple of af.Arrays</dt><dd><ul class="simple">
<li><p>L - Lower triangular matrix.</p></li>
<li><p>U - Upper triangular matrix.</p></li>
<li><p>P - Permutation array.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.lu_inplace">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">lu_inplace</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pivot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'lapack'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#lu_inplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.lu_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place LU decomposition.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>a 2 dimensional arrayfire array on entry.</p></li>
<li><p>Contains L in the lower triangle on exit.</p></li>
<li><p>Contains U in the upper triangle on exit.</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>P: af.Array</dt><dd><ul class="simple">
<li><p>Permutation array.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.norm">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">norm</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">A</span></em>, <em class="sig-param"><span class="pre">norm_type=<NORM.VECTOR_2:</span> <span class="pre">2></span></em>, <em class="sig-param"><span class="pre">p=1.0</span></em>, <em class="sig-param"><span class="pre">q=1.0</span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#norm"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 1 or 2 dimensional arrayfire array</p></li>
</ul>
</dd>
<dt><strong>norm_type: optional: af.NORM. default: af.NORM.EUCLID.</strong></dt><dd><ul class="simple">
<li><p>Type of norm to be calculated.</p></li>
</ul>
</dd>
<dt><strong>p: scalar. default 1.0.</strong></dt><dd><ul class="simple">
<li><p>Used only if <cite>norm_type</cite> is one of <cite>af.NORM.VECTOR_P</cite>, <cite>af.NORM_MATRIX_L_PQ</cite></p></li>
</ul>
</dd>
<dt><strong>q: scalar. default 1.0.</strong></dt><dd><ul class="simple">
<li><p>Used only if <cite>norm_type</cite> is <cite>af.NORM_MATRIX_L_PQ</cite></p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>res: scalar</dt><dd><ul class="simple">
<li><p>norm of the input</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.pinverse">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">pinverse</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">A</span></em>, <em class="sig-param"><span class="pre">tol=1e-06</span></em>, <em class="sig-param"><span class="pre">options=<MATPROP.NONE:</span> <span class="pre">0></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#pinverse"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.pinverse" title="Permalink to this definition">¶</a></dt>
<dd><p>Find pseudo-inverse(Moore-Penrose) of a matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 2 dimensional arrayfire input matrix array</p></li>
</ul>
</dd>
<dt><strong>tol: optional: scalar. default: 1E-6.</strong></dt><dd><ul class="simple">
<li><p>Tolerance for calculating rank</p></li>
</ul>
</dd>
<dt><strong>options: optional: af.MATPROP. default: af.MATPROP.NONE.</strong></dt><dd><ul class="simple">
<li><p>Currently needs to be <cite>af.MATPROP.NONE</cite>.</p></li>
<li><p>Additional options may speed up computation in the future</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>AI: af.Array</dt><dd><ul class="simple">
<li><p>A 2 dimensional array that is the pseudo-inverse of <cite>A</cite></p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.qr">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">qr</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#qr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.qr" title="Permalink to this definition">¶</a></dt>
<dd><p>QR decomposition.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional arrayfire array.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>(Q,R,T): tuple of af.Arrays</dt><dd><ul class="simple">
<li><p>Q - Orthogonal matrix.</p></li>
<li><p>R - Upper triangular matrix.</p></li>
<li><p>T - Vector containing additional information to solve a least squares problem.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.qr_inplace">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">qr_inplace</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#qr_inplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.qr_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>In place QR decomposition.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>a 2 dimensional arrayfire array on entry.</p></li>
<li><p>Packed Q and R matrices on exit.</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>T: af.Array</dt><dd><ul class="simple">
<li><p>Vector containing additional information to solve a least squares problem.</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.rank">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">rank</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#rank"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.rank" title="Permalink to this definition">¶</a></dt>
<dd><p>Rank of a matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 2 dimensional arrayfire array</p></li>
</ul>
</dd>
<dt><strong>tol: optional: scalar. default: 1E-5.</strong></dt><dd><ul class="simple">
<li><p>Tolerance for calculating rank</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>r: int</dt><dd><ul class="simple">
<li><p>Rank of <cite>A</cite> within the given tolerance</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.solve">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">solve</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">A</span></em>, <em class="sig-param"><span class="pre">B</span></em>, <em class="sig-param"><span class="pre">options=<MATPROP.NONE:</span> <span class="pre">0></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#solve"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional arrayfire array representing the coefficients of the system.</p>
</dd>
<dt><strong>B: af.Array</strong></dt><dd><p>A 1 or 2 dimensional arrayfire array representing the constants of the system.</p>
</dd>
<dt><strong>options: optional: af.MATPROP. default: af.MATPROP.NONE.</strong></dt><dd><ul class="simple">
<li><p>Additional options to speed up computations.</p></li>
<li><p>Currently needs to be one of <cite>af.MATPROP.NONE</cite>, <cite>af.MATPROP.LOWER</cite>, <cite>af.MATPROP.UPPER</cite>.</p></li>
</ul>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>X: af.Array</dt><dd><p>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.solve_lu">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">solve_lu</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">A</span></em>, <em class="sig-param"><span class="pre">P</span></em>, <em class="sig-param"><span class="pre">B</span></em>, <em class="sig-param"><span class="pre">options=<MATPROP.NONE:</span> <span class="pre">0></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#solve_lu"><span class="viewcode-link"><span class="pre">[source]</span></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>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><ul class="simple">
<li><p>A 2 dimensional arrayfire array representing the coefficients of the system.</p></li>
<li><p>This matrix should be decomposed previously using <cite>lu_inplace(A)</cite>.</p></li>
</ul>
</dd>
<dt><strong>P: af.Array</strong></dt><dd><ul class="simple">
<li><p>Permutation array.</p></li>
<li><p>This array is the output of an earlier call to <cite>lu_inplace(A)</cite></p></li>
</ul>
</dd>
<dt><strong>B: af.Array</strong></dt><dd><p>A 1 or 2 dimensional arrayfire array representing the constants of the system.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>X: af.Array</dt><dd><p>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.svd">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">svd</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#svd"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.svd" title="Permalink to this definition">¶</a></dt>
<dd><p>Singular Value Decomposition</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional arrayfire array.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>(U,S,Vt): tuple of af.Arrays</dt><dd><ul class="simple">
<li><p>U - A unitary matrix</p></li>
<li><p>S - An array containing the elements of diagonal matrix</p></li>
<li><p>Vt - A unitary matrix</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="arrayfire.lapack.svd_inplace">
<code class="sig-prename descclassname"><span class="pre">arrayfire.lapack.</span></code><code class="sig-name descname"><span class="pre">svd_inplace</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">A</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/arrayfire/lapack.html#svd_inplace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#arrayfire.lapack.svd_inplace" title="Permalink to this definition">¶</a></dt>
<dd><p>Singular Value Decomposition</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>A: af.Array</strong></dt><dd><p>A 2 dimensional arrayfire array.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt>(U,S,Vt): tuple of af.Arrays</dt><dd><ul class="simple">
<li><p>U - A unitary matrix</p></li>
<li><p>S - An array containing the elements of diagonal matrix</p></li>
<li><p>Vt - A unitary matrix</p></li>
</ul>
</dd>
</dl>
</dd>
</dl>
</dd></dl>
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