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| <div class="section" id="linear-algebra-ndarray-api"> |
| <span id="linear-algebra-ndarray-api"></span><h1>Linear Algebra NDArray API<a class="headerlink" href="#linear-algebra-ndarray-api" title="Permalink to this headline">¶</a></h1> |
| <div class="section" id="overview"> |
| <span id="overview"></span><h2>Overview<a class="headerlink" href="#overview" title="Permalink to this headline">¶</a></h2> |
| <p>This document lists the linear algebra routines of the <em>n</em>-dimensional array package:</p> |
| <table border="1" class="longtable docutils"> |
| <colgroup> |
| <col width="10%"/> |
| <col width="90%"/> |
| </colgroup> |
| <tbody valign="top"> |
| <tr class="row-odd"><td><a class="reference internal" href="#module-mxnet.ndarray.linalg" title="mxnet.ndarray.linalg"><code class="xref py py-obj docutils literal"><span class="pre">mxnet.ndarray.linalg</span></code></a></td> |
| <td>Linear Algebra NDArray API of MXNet.</td> |
| </tr> |
| </tbody> |
| </table> |
| <p>The <code class="docutils literal"><span class="pre">Linear</span> <span class="pre">Algebra</span> <span class="pre">NDArray</span></code> API, defined in the <code class="docutils literal"><span class="pre">ndarray.linalg</span></code> package, provides |
| imperative linear algebra tensor operations on CPU/GPU.</p> |
| <p>In the rest of this document, we list routines provided by the <code class="docutils literal"><span class="pre">ndarray.linalg</span></code> package.</p> |
| </div> |
| <div class="section" id="linear-algebra"> |
| <span id="linear-algebra"></span><h2>Linear Algebra<a class="headerlink" href="#linear-algebra" title="Permalink to this headline">¶</a></h2> |
| <table border="1" class="longtable docutils"> |
| <colgroup> |
| <col width="10%"/> |
| <col width="90%"/> |
| </colgroup> |
| <tbody valign="top"> |
| <tr class="row-odd"><td><a class="reference internal" href="#mxnet.ndarray.linalg.gemm" title="mxnet.ndarray.linalg.gemm"><code class="xref py py-obj docutils literal"><span class="pre">gemm</span></code></a></td> |
| <td>Performs general matrix multiplication and accumulation.</td> |
| </tr> |
| <tr class="row-even"><td><a class="reference internal" href="#mxnet.ndarray.linalg.gemm2" title="mxnet.ndarray.linalg.gemm2"><code class="xref py py-obj docutils literal"><span class="pre">gemm2</span></code></a></td> |
| <td>Performs general matrix multiplication.</td> |
| </tr> |
| <tr class="row-odd"><td><a class="reference internal" href="#mxnet.ndarray.linalg.potrf" title="mxnet.ndarray.linalg.potrf"><code class="xref py py-obj docutils literal"><span class="pre">potrf</span></code></a></td> |
| <td>Performs Cholesky factorization of a symmetric positive-definite matrix.</td> |
| </tr> |
| <tr class="row-even"><td><a class="reference internal" href="#mxnet.ndarray.linalg.potri" title="mxnet.ndarray.linalg.potri"><code class="xref py py-obj docutils literal"><span class="pre">potri</span></code></a></td> |
| <td>Performs matrix inversion from a Cholesky factorization.</td> |
| </tr> |
| <tr class="row-odd"><td><a class="reference internal" href="#mxnet.ndarray.linalg.trmm" title="mxnet.ndarray.linalg.trmm"><code class="xref py py-obj docutils literal"><span class="pre">trmm</span></code></a></td> |
| <td>Performs multiplication with a lower triangular matrix.</td> |
| </tr> |
| <tr class="row-even"><td><a class="reference internal" href="#mxnet.ndarray.linalg.trsm" title="mxnet.ndarray.linalg.trsm"><code class="xref py py-obj docutils literal"><span class="pre">trsm</span></code></a></td> |
| <td>Solves matrix equation involving a lower triangular matrix.</td> |
| </tr> |
| <tr class="row-odd"><td><a class="reference internal" href="#mxnet.ndarray.linalg.sumlogdiag" title="mxnet.ndarray.linalg.sumlogdiag"><code class="xref py py-obj docutils literal"><span class="pre">sumlogdiag</span></code></a></td> |
| <td>Computes the sum of the logarithms of the diagonal elements of a square matrix.</td> |
| </tr> |
| <tr class="row-even"><td><a class="reference internal" href="#mxnet.ndarray.linalg.syrk" title="mxnet.ndarray.linalg.syrk"><code class="xref py py-obj docutils literal"><span class="pre">syrk</span></code></a></td> |
| <td>Multiplication of matrix with its transpose.</td> |
| </tr> |
| <tr class="row-odd"><td><a class="reference internal" href="#mxnet.ndarray.linalg.gelqf" title="mxnet.ndarray.linalg.gelqf"><code class="xref py py-obj docutils literal"><span class="pre">gelqf</span></code></a></td> |
| <td>LQ factorization for general matrix.</td> |
| </tr> |
| <tr class="row-even"><td><a class="reference internal" href="#mxnet.ndarray.linalg.syevd" title="mxnet.ndarray.linalg.syevd"><code class="xref py py-obj docutils literal"><span class="pre">syevd</span></code></a></td> |
| <td>Eigendecomposition for symmetric matrix.</td> |
| </tr> |
| </tbody> |
| </table> |
| </div> |
| <div class="section" id="api-reference"> |
| <span id="api-reference"></span><h2>API Reference<a class="headerlink" href="#api-reference" title="Permalink to this headline">¶</a></h2> |
| <script src="../../../_static/js/auto_module_index.js" type="text/javascript"></script><span class="target" id="module-mxnet.ndarray.linalg"></span><p>Linear Algebra NDArray API of MXNet.</p> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gelqf"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">gelqf</code><span class="sig-paren">(</span><em>A=None</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gelqf" title="Permalink to this definition">¶</a></dt> |
| <dd><p>LQ factorization for general matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, we compute the LQ factorization (LAPACK <em>gelqf</em>, followed by <em>orglq</em>). <em>A</em> |
| must have shape <em>(x, y)</em> with <em>x <= y</em>, and must have full rank <em>=x</em>. The LQ |
| factorization consists of <em>L</em> with shape <em>(x, x)</em> and <em>Q</em> with shape <em>(x, y)</em>, so |
| that:</p> |
| <blockquote> |
| <div><em>A</em> = <em>L</em> * <em>Q</em></div></blockquote> |
| <p>Here, <em>L</em> is lower triangular (upper triangle equal to zero) with nonzero diagonal, |
| and <em>Q</em> is row-orthonormal, meaning that</p> |
| <blockquote> |
| <div><em>Q</em> * <em>Q</em><sup>T</sup></div></blockquote> |
| <p>is equal to the identity matrix of shape <em>(x, x)</em>.</p> |
| <p>If <em>n>2</em>, <em>gelqf</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">LQ</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]]</span> |
| <span class="n">Q</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">gelqf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">Q</span> <span class="o">=</span> <span class="p">[[</span><span class="o">-</span><span class="mf">0.26726124</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.53452248</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.80178373</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.87287156</span><span class="p">,</span> <span class="mf">0.21821789</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.43643578</span><span class="p">]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[</span><span class="o">-</span><span class="mf">3.74165739</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">8.55235974</span><span class="p">,</span> <span class="mf">1.96396101</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">LQ</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">7.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">],</span> <span class="p">[</span><span class="mf">10.</span><span class="p">,</span> <span class="mf">11.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">]]]</span> |
| <span class="n">Q</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">gelqf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">Q</span> <span class="o">=</span> <span class="p">[[[</span><span class="o">-</span><span class="mf">0.26726124</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.53452248</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.80178373</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.87287156</span><span class="p">,</span> <span class="mf">0.21821789</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.43643578</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="o">-</span><span class="mf">0.50257071</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.57436653</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.64616234</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.7620735</span><span class="p">,</span> <span class="mf">0.05862104</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.64483142</span><span class="p">]]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[[</span><span class="o">-</span><span class="mf">3.74165739</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">8.55235974</span><span class="p">,</span> <span class="mf">1.96396101</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="o">-</span><span class="mf">13.92838828</span><span class="p">,</span> <span class="mf">0.</span><span class="p">],</span> |
| <span class="p">[</span><span class="o">-</span><span class="mf">19.09768702</span><span class="p">,</span> <span class="mf">0.52758934</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L552</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be factorized</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gemm"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">gemm</code><span class="sig-paren">(</span><em>A=None</em>, <em>B=None</em>, <em>C=None</em>, <em>transpose_a=_Null</em>, <em>transpose_b=_Null</em>, <em>alpha=_Null</em>, <em>beta=_Null</em>, <em>axis=_Null</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gemm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs general matrix multiplication and accumulation. |
| Input are tensors <em>A</em>, <em>B</em>, <em>C</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, the BLAS3 function <em>gemm</em> is performed:</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>op</em>(<em>B</em>) + <em>beta</em> * <em>C</em></div></blockquote> |
| <p>Here, <em>alpha</em> and <em>beta</em> are scalar parameters, and <em>op()</em> is either the identity or |
| matrix transposition (depending on <em>transpose_a</em>, <em>transpose_b</em>).</p> |
| <p>If <em>n>2</em>, <em>gemm</em> is performed separately for a batch of matrices. The column indices of the matrices |
| are given by the last dimensions of the tensors, the row indices by the axis specified with the <em>axis</em> |
| parameter. By default, the trailing two dimensions will be used for matrix encoding.</p> |
| <p>For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes |
| calls. For example let <em>A</em>, <em>B</em>, <em>C</em> be 5 dimensional tensors. Then gemm(<em>A</em>, <em>B</em>, <em>C</em>, axis=1) is equivalent to</p> |
| <blockquote> |
| <div>A1 = swapaxes(A, dim1=1, dim2=3) |
| B1 = swapaxes(B, dim1=1, dim2=3) |
| C = swapaxes(C, dim1=1, dim2=3) |
| C = gemm(A1, B1, C) |
| C = swapaxis(C, dim1=1, dim2=3)</div></blockquote> |
| <p>without the overhead of the additional swapaxis operations.</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span><span class="o">-</span><span class="n">add</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">gemm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="mf">10.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">,</span> <span class="mf">14.0</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span><span class="o">-</span><span class="n">add</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">C</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">10.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.01</span><span class="p">]]]</span> |
| <span class="n">gemm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span> <span class="p">,</span> <span class="n">beta</span><span class="o">=</span><span class="mf">10.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[[</span><span class="mf">104.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.14</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L81</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>B</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>C</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>transpose_a</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of first input (A).</li> |
| <li><strong>transpose_b</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of second input (B).</li> |
| <li><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with A*B.</li> |
| <li><strong>beta</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with C.</li> |
| <li><strong>axis</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='-2'</em>) – Axis corresponding to the matrix rows.</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.gemm2"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">gemm2</code><span class="sig-paren">(</span><em>A=None</em>, <em>B=None</em>, <em>transpose_a=_Null</em>, <em>transpose_b=_Null</em>, <em>alpha=_Null</em>, <em>axis=_Null</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.gemm2" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs general matrix multiplication. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, the BLAS3 function <em>gemm</em> is performed:</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>op</em>(<em>B</em>)</div></blockquote> |
| <p>Here <em>alpha</em> is a scalar parameter and <em>op()</em> is either the identity or the matrix |
| transposition (depending on <em>transpose_a</em>, <em>transpose_b</em>).</p> |
| <p>If <em>n>2</em>, <em>gemm</em> is performed separately for a batch of matrices. The column indices of the matrices |
| are given by the last dimensions of the tensors, the row indices by the axis specified with the <em>axis</em> |
| parameter. By default, the trailing two dimensions will be used for matrix encoding.</p> |
| <p>For a non-default axis parameter, the operation performed is equivalent to a series of swapaxes/gemm/swapaxes |
| calls. For example let <em>A</em>, <em>B</em> be 5 dimensional tensors. Then gemm(<em>A</em>, <em>B</em>, axis=1) is equivalent to</p> |
| <blockquote> |
| <div>A1 = swapaxes(A, dim1=1, dim2=3) |
| B1 = swapaxes(B, dim1=1, dim2=3) |
| C = gemm2(A1, B1) |
| C = swapaxis(C, dim1=1, dim2=3)</div></blockquote> |
| <p>without the overhead of the additional swapaxis operations.</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">gemm2</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">gemm2</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">transpose_b</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.04</span> <span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L151</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>B</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>transpose_a</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of first input (A).</li> |
| <li><strong>transpose_b</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply with transposed of second input (B).</li> |
| <li><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor multiplied with A*B.</li> |
| <li><strong>axis</strong> (<em>int</em><em>, </em><em>optional</em><em>, </em><em>default='-2'</em>) – Axis corresponding to the matrix row indices.</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.potrf"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">potrf</code><span class="sig-paren">(</span><em>A=None</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.potrf" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs Cholesky factorization of a symmetric positive-definite matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, the Cholesky factor <em>L</em> of the symmetric, positive definite matrix <em>A</em> is |
| computed. <em>L</em> is lower triangular (entries of upper triangle are all zero), has |
| positive diagonal entries, and:</p> |
| <blockquote> |
| <div><em>A</em> = <em>L</em> * <em>L</em><sup>T</sup></div></blockquote> |
| <p>If <em>n>2</em>, <em>potrf</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.25</span><span class="p">]]</span> |
| <span class="n">potrf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">factorization</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.25</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">16.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">17.0</span><span class="p">]]]</span> |
| <span class="n">potrf</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L201</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be decomposed</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.potri"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">potri</code><span class="sig-paren">(</span><em>A=None</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.potri" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs matrix inversion from a Cholesky factorization. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> is a lower triangular matrix (entries of upper triangle are all zero) |
| with positive diagonal. We compute:</p> |
| <blockquote> |
| <div><em>out</em> = <em>A</em><sup>-T</sup> * <em>A</em><sup>-1</sup></div></blockquote> |
| <p>In other words, if <em>A</em> is the Cholesky factor of a symmetric positive definite matrix |
| <em>B</em> (obtained by <em>potrf</em>), then</p> |
| <blockquote> |
| <div><em>out</em> = <em>B</em><sup>-1</sup></div></blockquote> |
| <p>If <em>n>2</em>, <em>potri</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">Use this operator only if you are certain you need the inverse of <em>B</em>, and |
| cannot use the Cholesky factor <em>A</em> (<em>potrf</em>), together with backsubstitution |
| (<em>trsm</em>). The latter is numerically much safer, and also cheaper.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]</span> |
| <span class="n">potri</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.26563</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0625</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.0625</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">inverse</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]]</span> |
| <span class="n">potri</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">0.26563</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0625</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.0625</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">0.06641</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.01562</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.01562</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span><span class="mi">0625</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L259</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.sumlogdiag"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">sumlogdiag</code><span class="sig-paren">(</span><em>A=None</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.sumlogdiag" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Computes the sum of the logarithms of the diagonal elements of a square matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be square with positive diagonal entries. We sum the natural |
| logarithms of the diagonal elements, the result has shape (1,).</p> |
| <p>If <em>n>2</em>, <em>sumlogdiag</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">reduction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">]]</span> |
| <span class="n">sumlogdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.9459</span><span class="p">]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">reduction</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">7.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">17.0</span><span class="p">]]]</span> |
| <span class="n">sumlogdiag</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.9459</span><span class="p">,</span> <span class="mf">3.9318</span><span class="p">]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L428</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of square matrices</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.syevd"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">syevd</code><span class="sig-paren">(</span><em>A=None</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.syevd" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Eigendecomposition for symmetric matrix. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be symmetric, of shape <em>(x, x)</em>. We compute the eigendecomposition, |
| resulting in the orthonormal matrix <em>U</em> of eigenvectors, shape <em>(x, x)</em>, and the |
| vector <em>L</em> of eigenvalues, shape <em>(x,)</em>, so that:</p> |
| <blockquote> |
| <div><em>U</em> * <em>A</em> = <em>diag(L)</em> * <em>U</em></div></blockquote> |
| <p>Here:</p> |
| <blockquote> |
| <div><em>U</em> * <em>U</em><sup>T</sup> = <em>U</em><sup>T</sup> * <em>U</em> = <em>I</em></div></blockquote> |
| <p>where <em>I</em> is the identity matrix. Also, <em>L(0) <= L(1) <= L(2) <= ...</em> (ascending order).</p> |
| <p>If <em>n>2</em>, <em>syevd</em> is performed separately on the trailing two dimensions of <em>A</em> (batch |
| mode). In this case, <em>U</em> has <em>n</em> dimensions like <em>A</em>, and <em>L</em> has <em>n-1</em> dimensions.</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">Derivatives for this operator are defined only if <em>A</em> is such that all its |
| eigenvalues are distinct, and the eigengaps are not too small. If you need |
| gradients, do not apply this operator to matrices with multiple eigenvalues.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">symmetric</span> <span class="n">eigendecomposition</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]]</span> |
| <span class="n">U</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">syevd</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">U</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.89442719</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.4472136</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.4472136</span><span class="p">,</span> <span class="mf">0.89442719</span><span class="p">]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">symmetric</span> <span class="n">eigendecomposition</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">]]]</span> |
| <span class="n">U</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="n">syevd</span><span class="p">(</span><span class="n">A</span><span class="p">)</span> |
| <span class="n">U</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">0.89442719</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.4472136</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.4472136</span><span class="p">,</span> <span class="mf">0.89442719</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">0.92387953</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.38268343</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.38268343</span><span class="p">,</span> <span class="mf">0.92387953</span><span class="p">]]]</span> |
| <span class="n">L</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">0.17157288</span><span class="p">,</span> <span class="mf">5.82842712</span><span class="p">]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L621</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices to be factorized</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.syrk"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">syrk</code><span class="sig-paren">(</span><em>A=None</em>, <em>transpose=_Null</em>, <em>alpha=_Null</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.syrk" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Multiplication of matrix with its transpose. |
| Input is a tensor <em>A</em> of dimension <em>n >= 2</em>.</p> |
| <p>If <em>n=2</em>, the operator performs the BLAS3 function <em>syrk</em>:</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>A</em> * <em>A</em><sup>T</sup></div></blockquote> |
| <p>if <em>transpose=False</em>, or</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>A</em><sup>T</sup> * <em>A</em></div></blockquote> |
| <p>if <em>transpose=True</em>.</p> |
| <p>If <em>n>2</em>, <em>syrk</em> is performed separately on the trailing two dimensions for all |
| inputs (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">14.</span><span class="p">,</span> <span class="mf">32.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">32.</span><span class="p">,</span> <span class="mf">77.</span><span class="p">]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">1.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span> |
| <span class="o">=</span> <span class="p">[[</span><span class="mf">17.</span><span class="p">,</span> <span class="mf">22.</span><span class="p">,</span> <span class="mf">27.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">22.</span><span class="p">,</span> <span class="mf">29.</span><span class="p">,</span> <span class="mf">36.</span><span class="p">],</span> |
| <span class="p">[</span><span class="mf">27.</span><span class="p">,</span> <span class="mf">36.</span><span class="p">,</span> <span class="mf">45.</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]]]</span> |
| <span class="n">syrk</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.</span><span class="p">,</span> <span class="n">transpose</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">4.</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.04</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L484</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of input matrices</li> |
| <li><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transpose of input matrix.</li> |
| <li><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.trmm"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">trmm</code><span class="sig-paren">(</span><em>A=None</em>, <em>B=None</em>, <em>transpose=_Null</em>, <em>rightside=_Null</em>, <em>alpha=_Null</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.trmm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Performs multiplication with a lower triangular matrix. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be lower triangular. The operator performs the BLAS3 function |
| <em>trmm</em>:</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>op</em>(<em>A</em>) * <em>B</em></div></blockquote> |
| <p>if <em>rightside=False</em>, or</p> |
| <blockquote> |
| <div><em>out</em> = <em>alpha</em> * <em>B</em> * <em>op</em>(<em>A</em>)</div></blockquote> |
| <p>if <em>rightside=True</em>. Here, <em>alpha</em> is a scalar parameter, and <em>op()</em> is either the |
| identity or the matrix transposition (depending on <em>transpose</em>).</p> |
| <p>If <em>n>2</em>, <em>trmm</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">triangular</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">trmm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">triangular</span> <span class="n">matrix</span> <span class="n">multiply</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]]]</span> |
| <span class="n">trmm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">2.0</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L316</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</li> |
| <li><strong>B</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of matrices</li> |
| <li><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transposed of the triangular matrix</li> |
| <li><strong>rightside</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</li> |
| <li><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| </dd></dl> |
| <dl class="function"> |
| <dt id="mxnet.ndarray.linalg.trsm"> |
| <code class="descclassname">mxnet.ndarray.linalg.</code><code class="descname">trsm</code><span class="sig-paren">(</span><em>A=None</em>, <em>B=None</em>, <em>transpose=_Null</em>, <em>rightside=_Null</em>, <em>alpha=_Null</em>, <em>out=None</em>, <em>name=None</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#mxnet.ndarray.linalg.trsm" title="Permalink to this definition">¶</a></dt> |
| <dd><p>Solves matrix equation involving a lower triangular matrix. |
| Input are tensors <em>A</em>, <em>B</em>, each of dimension <em>n >= 2</em> and having the same shape |
| on the leading <em>n-2</em> dimensions.</p> |
| <p>If <em>n=2</em>, <em>A</em> must be lower triangular. The operator performs the BLAS3 function |
| <em>trsm</em>, solving for <em>out</em> in:</p> |
| <blockquote> |
| <div><em>op</em>(<em>A</em>) * <em>out</em> = <em>alpha</em> * <em>B</em></div></blockquote> |
| <p>if <em>rightside=False</em>, or</p> |
| <blockquote> |
| <div><em>out</em> * <em>op</em>(<em>A</em>) = <em>alpha</em> * <em>B</em></div></blockquote> |
| <p>if <em>rightside=True</em>. Here, <em>alpha</em> is a scalar parameter, and <em>op()</em> is either the |
| identity or the matrix transposition (depending on <em>transpose</em>).</p> |
| <p>If <em>n>2</em>, <em>trsm</em> is performed separately on the trailing two dimensions for all inputs |
| (batch mode).</p> |
| <div class="admonition note"> |
| <p class="first admonition-title">Note</p> |
| <p class="last">The operator supports float32 and float64 data types only.</p> |
| </div> |
| <p>Examples:</p> |
| <div class="highlight-default"><div class="highlight"><pre><span></span><span class="o">//</span> <span class="n">Single</span> <span class="n">matrix</span> <span class="n">solve</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]]</span> |
| <span class="n">trsm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]</span> |
| |
| <span class="o">//</span> <span class="n">Batch</span> <span class="n">matrix</span> <span class="n">solve</span> |
| <span class="n">A</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> <span class="p">[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]]]</span> |
| <span class="n">B</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">8.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">,</span> <span class="mf">8.0</span><span class="p">]]]</span> |
| <span class="n">trsm</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]],</span> |
| <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]]]</span> |
| </pre></div> |
| </div> |
| <p>Defined in src/operator/tensor/la_op.cc:L379</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"><ul class="first simple"> |
| <li><strong>A</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of lower triangular matrices</li> |
| <li><strong>B</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a>) – Tensor of matrices</li> |
| <li><strong>transpose</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Use transposed of the triangular matrix</li> |
| <li><strong>rightside</strong> (<em>boolean</em><em>, </em><em>optional</em><em>, </em><em>default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</li> |
| <li><strong>alpha</strong> (<em>double</em><em>, </em><em>optional</em><em>, </em><em>default=1</em>) – Scalar factor to be applied to the result.</li> |
| <li><strong>out</strong> (<a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray"><em>NDArray</em></a><em>, </em><em>optional</em>) – The output NDArray to hold the result.</li> |
| </ul> |
| </td> |
| </tr> |
| <tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>out</strong> – The output of this function.</p> |
| </td> |
| </tr> |
| <tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference internal" href="ndarray.html#mxnet.ndarray.NDArray" title="mxnet.ndarray.NDArray">NDArray</a> or list of NDArrays</p> |
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