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<!DOCTYPE html>

<html>

<head>

<title>arrayfire.lapack module — ArrayFire Python documentation</title>

</head><body>

<h1>arrayfire.lapack module<a class="headerlink" href="#module-arrayfire.lapack" title="Permalink to this headline">¶</a></h1>

Dense Linear Algebra functions (solve, inverse, etc).

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">cholesky</code>(A, is_upper=True)<a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky">[source]</a><a class="headerlink" href="#arrayfire.lapack.cholesky" title="Permalink to this definition">¶</a></dt>

<dd>Cholesky decomposition

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional, symmetric, positive definite matrix.

</dd>

<dt>is_upper: optional: bool. default: True</dt><dd>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>(R,info): tuple of af.Array, int.</dt><dd><ul class="simple">

<li>R - triangular matrix.</li>

<li>info - 0 if decomposition sucessful.</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">cholesky_inplace</code>(A, is_upper=True)<a class="reference internal" href="_modules/arrayfire/lapack.html#cholesky_inplace">[source]</a><a class="headerlink" href="#arrayfire.lapack.cholesky_inplace" title="Permalink to this definition">¶</a></dt>

<dd>In place Cholesky decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>a 2 dimensional, symmetric, positive definite matrix.</li>

<li>Trinangular matrix on exit.</li>

</ul>

</dd>

<dt>is_upper: optional: bool. default: True.</dt><dd>Specifies if output <cite>R</cite> is upper triangular (if True) or lower triangular (if False).

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>infoint.</dt><dd>0 if decomposition sucessful.

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">det</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#det">[source]</a><a class="headerlink" href="#arrayfire.lapack.det" title="Permalink to this definition">¶</a></dt>

<dd>Determinant of a matrix.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional arrayfire array</li>

</ul>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>res: scalar</dt><dd><ul class="simple">

<li>Determinant of the matrix.</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">inverse</code>(A, options=<MATPROP.NONE: 0>)<a class="reference internal" href="_modules/arrayfire/lapack.html#inverse">[source]</a><a class="headerlink" href="#arrayfire.lapack.inverse" title="Permalink to this definition">¶</a></dt>

<dd>Invert a matrix.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional arrayfire array</li>

</ul>

</dd>

<dt>options: optional: af.MATPROP. default: af.MATPROP.NONE.</dt><dd><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>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>AI: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional array that is the inverse of <cite>A</cite></li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">is_lapack_available</code>()<a class="reference internal" href="_modules/arrayfire/lapack.html#is_lapack_available">[source]</a><a class="headerlink" href="#arrayfire.lapack.is_lapack_available" title="Permalink to this definition">¶</a></dt>

<dd>Function to check if the arrayfire library was built with lapack support.

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">lu</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#lu">[source]</a><a class="headerlink" href="#arrayfire.lapack.lu" title="Permalink to this definition">¶</a></dt>

<dd>LU decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional arrayfire array.

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>(L,U,P): tuple of af.Arrays</dt><dd><ul class="simple">

<li>L - Lower triangular matrix.</li>

<li>U - Upper triangular matrix.</li>

<li>P - Permutation array.</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">lu_inplace</code>(A, pivot='lapack')<a class="reference internal" href="_modules/arrayfire/lapack.html#lu_inplace">[source]</a><a class="headerlink" href="#arrayfire.lapack.lu_inplace" title="Permalink to this definition">¶</a></dt>

<dd>In place LU decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><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>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>P: af.Array</dt><dd><ul class="simple">

<li>Permutation array.</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">norm</code>(A, norm_type=<NORM.VECTOR_2: 2>, p=1.0, q=1.0)<a class="reference internal" href="_modules/arrayfire/lapack.html#norm">[source]</a><a class="headerlink" href="#arrayfire.lapack.norm" title="Permalink to this definition">¶</a></dt>

<dd>Norm of an array or a matrix.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>A 1 or 2 dimensional arrayfire array</li>

</ul>

</dd>

<dt>norm_type: optional: af.NORM. default: af.NORM.EUCLID.</dt><dd><ul class="simple">

<li>Type of norm to be calculated.</li>

</ul>

</dd>

<dt>p: scalar. default 1.0.</dt><dd><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>

</dd>

<dt>q: scalar. default 1.0.</dt><dd><ul class="simple">

<li>Used only if <cite>norm_type</cite> is <cite>af.NORM_MATRIX_L_PQ</cite></li>

</ul>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>res: scalar</dt><dd><ul class="simple">

<li>norm of the input</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">pinverse</code>(A, tol=1e-06, options=<MATPROP.NONE: 0>)<a class="reference internal" href="_modules/arrayfire/lapack.html#pinverse">[source]</a><a class="headerlink" href="#arrayfire.lapack.pinverse" title="Permalink to this definition">¶</a></dt>

<dd>Find pseudo-inverse(Moore-Penrose) of a matrix.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional arrayfire input matrix array</li>

</ul>

</dd>

<dt>tol: optional: scalar. default: 1E-6.</dt><dd><ul class="simple">

<li>Tolerance for calculating rank</li>

</ul>

</dd>

<dt>options: optional: af.MATPROP. default: af.MATPROP.NONE.</dt><dd><ul class="simple">

<li>Currently needs to be <cite>af.MATPROP.NONE</cite>.</li>

<li>Additional options may speed up computation in the future</li>

</ul>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>AI: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional array that is the pseudo-inverse of <cite>A</cite></li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">qr</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#qr">[source]</a><a class="headerlink" href="#arrayfire.lapack.qr" title="Permalink to this definition">¶</a></dt>

<dd>QR decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional arrayfire array.

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>(Q,R,T): tuple of af.Arrays</dt><dd><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>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">qr_inplace</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#qr_inplace">[source]</a><a class="headerlink" href="#arrayfire.lapack.qr_inplace" title="Permalink to this definition">¶</a></dt>

<dd>In place QR decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>a 2 dimensional arrayfire array on entry.</li>

<li>Packed Q and R matrices on exit.</li>

</ul>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>T: af.Array</dt><dd><ul class="simple">

<li>Vector containing additional information to solve a least squares problem.</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">rank</code>(A, tol=1e-05)<a class="reference internal" href="_modules/arrayfire/lapack.html#rank">[source]</a><a class="headerlink" href="#arrayfire.lapack.rank" title="Permalink to this definition">¶</a></dt>

<dd>Rank of a matrix.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><ul class="simple">

<li>A 2 dimensional arrayfire array</li>

</ul>

</dd>

<dt>tol: optional: scalar. default: 1E-5.</dt><dd><ul class="simple">

<li>Tolerance for calculating rank</li>

</ul>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<li>Rank of <cite>A</cite> within the given tolerance</li>

</ul>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">solve</code>(A, B, options=<MATPROP.NONE: 0>)<a class="reference internal" href="_modules/arrayfire/lapack.html#solve">[source]</a><a class="headerlink" href="#arrayfire.lapack.solve" title="Permalink to this definition">¶</a></dt>

<dd>Solve a system of linear equations.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional arrayfire array representing the coefficients of the system.

</dd>

<dt>B: af.Array</dt><dd>A 1 or 2 dimensional arrayfire array representing the constants of the system.

</dd>

<dt>options: optional: af.MATPROP. default: af.MATPROP.NONE.</dt><dd><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>

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>X: af.Array</dt><dd>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">solve_lu</code>(A, P, B, options=<MATPROP.NONE: 0>)<a class="reference internal" href="_modules/arrayfire/lapack.html#solve_lu">[source]</a><a class="headerlink" href="#arrayfire.lapack.solve_lu" title="Permalink to this definition">¶</a></dt>

<dd>Solve a system of linear equations, using LU decomposition.

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd><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>

</dd>

<dt>P: af.Array</dt><dd><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>

</dd>

<dt>B: af.Array</dt><dd>A 1 or 2 dimensional arrayfire array representing the constants of the system.

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>X: af.Array</dt><dd>A 1 or 2 dimensional arrayfire array representing the unknowns in the system.

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">svd</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#svd">[source]</a><a class="headerlink" href="#arrayfire.lapack.svd" title="Permalink to this definition">¶</a></dt>

<dd>Singular Value Decomposition

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional arrayfire array.

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>(U,S,Vt): tuple of af.Arrays</dt><dd><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>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

<code class="sig-prename descclassname">arrayfire.lapack.</code><code class="sig-name descname">svd_inplace</code>(A)<a class="reference internal" href="_modules/arrayfire/lapack.html#svd_inplace">[source]</a><a class="headerlink" href="#arrayfire.lapack.svd_inplace" title="Permalink to this definition">¶</a></dt>

<dd>Singular Value Decomposition

<dt class="field-odd">Parameters</dt>

<dt>A: af.Array</dt><dd>A 2 dimensional arrayfire array.

</dd>

</dl>

</dd>

<dt class="field-even">Returns</dt>

<dt>(U,S,Vt): tuple of af.Arrays</dt><dd><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>

</dd>

</dl>

</dd>

</dl>

</dd></dl>

</div>

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<h3>Navigation</h3>

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<li><a href="index.html">Documentation overview</a><ul>

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& <a href="https://github.com/bitprophet/alabaster">Alabaster 0.7.12</a>

<a href="_sources/arrayfire.lapack.rst.txt"

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