Google Git
Sign in
apache / mxnet-site / refs/heads/test-revert / . / versions / 0.12.0 / api / python / ndarray / linalg.html
blob: c5f029810de03c21240b01d6fcd498b4d16d4ea9 [file] [log] [blame]
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<meta content="IE=edge" http-equiv="X-UA-Compatible"/>
<meta content="width=device-width, initial-scale=1" name="viewport"/>
<title>Linear Algebra NDArray API — mxnet documentation</title>
<link crossorigin="anonymous" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" integrity="sha384-1q8mTJOASx8j1Au+a5WDVnPi2lkFfwwEAa8hDDdjZlpLegxhjVME1fgjWPGmkzs7" rel="stylesheet"/>
<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.5.0/css/font-awesome.min.css" rel="stylesheet"/>
<link href="../../../_static/basic.css" rel="stylesheet" type="text/css"/>
<link href="../../../_static/pygments.css" rel="stylesheet" type="text/css"/>
<link href="../../../_static/mxnet.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: '../../../',
VERSION: '',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true,
SOURCELINK_SUFFIX: ''
};
</script>
<script src="../../../_static/jquery-1.11.1.js" type="text/javascript"></script>
<script src="../../../_static/underscore.js" type="text/javascript"></script>
<script src="../../../_static/searchtools_custom.js" type="text/javascript"></script>
<script src="../../../_static/doctools.js" type="text/javascript"></script>
<script src="../../../_static/selectlang.js" type="text/javascript"></script>
<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
<script type="text/javascript"> jQuery(function() { Search.loadIndex("/searchindex.js"); Search.init();}); </script>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new
Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-96378503-1', 'auto');
ga('send', 'pageview');
</script>
<!-- -->
<!-- <script type="text/javascript" src="../../../_static/jquery.js"></script> -->
<!-- -->
<!-- <script type="text/javascript" src="../../../_static/underscore.js"></script> -->
<!-- -->
<!-- <script type="text/javascript" src="../../../_static/doctools.js"></script> -->
<!-- -->
<!-- <script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> -->
<!-- -->
<link href="../index.html" rel="up" title="MXNet - Python API">
<link href="sparse.html" rel="next" title="Sparse NDArray API"/>
<link href="random.html" rel="prev" title="Random Distribution Generator NDArray API"/>
<link href="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/mxnet-icon.png" rel="icon" type="image/png">
</link></link></head>
<body background="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/mxnet-background-compressed.jpeg" role="document">
<div class="content-block"><div class="navbar navbar-fixed-top">
<div class="container" id="navContainer">
<div class="innder" id="header-inner">
<h1 id="logo-wrap">
<a href="../../../" id="logo"><img src="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/mxnet_logo.png"/></a>
</h1>
<nav class="nav-bar" id="main-nav">
<a class="main-nav-link" href="../../../install/index.html">Install</a>
<a class="main-nav-link" href="../../../tutorials/index.html">Tutorials</a>
<span id="dropdown-menu-position-anchor">
<a aria-expanded="true" aria-haspopup="true" class="main-nav-link dropdown-toggle" data-toggle="dropdown" href="#" role="button">Gluon <span class="caret"></span></a>
<ul class="dropdown-menu navbar-menu" id="package-dropdown-menu">
<li><a class="main-nav-link" href="../../../gluon/index.html">About</a></li>
<li><a class="main-nav-link" href="http://gluon.mxnet.io">Tutorials</a></li>
</ul>
</span>
<span id="dropdown-menu-position-anchor">
<a aria-expanded="true" aria-haspopup="true" class="main-nav-link dropdown-toggle" data-toggle="dropdown" href="#" role="button">API <span class="caret"></span></a>
<ul class="dropdown-menu navbar-menu" id="package-dropdown-menu">
<li><a class="main-nav-link" href="../../../api/python/index.html">Python</a></li>
<li><a class="main-nav-link" href="../../../api/scala/index.html">Scala</a></li>
<li><a class="main-nav-link" href="../../../api/r/index.html">R</a></li>
<li><a class="main-nav-link" href="../../../api/julia/index.html">Julia</a></li>
<li><a class="main-nav-link" href="../../../api/c++/index.html">C++</a></li>
<li><a class="main-nav-link" href="../../../api/perl/index.html">Perl</a></li>
</ul>
</span>
<span id="dropdown-menu-position-anchor-docs">
<a aria-expanded="true" aria-haspopup="true" class="main-nav-link dropdown-toggle" data-toggle="dropdown" href="#" role="button">Docs <span class="caret"></span></a>
<ul class="dropdown-menu navbar-menu" id="package-dropdown-menu-docs">
<li><a class="main-nav-link" href="../../../faq/index.html">FAQ</a></li>
<li><a class="main-nav-link" href="../../../architecture/index.html">Architecture</a></li>
<li><a class="main-nav-link" href="https://github.com/apache/incubator-mxnet/tree/0.12.0/example">Examples</a></li>
<li><a class="main-nav-link" href="../../../model_zoo/index.html">Model Zoo</a></li>
</ul>
</span>
<a class="main-nav-link" href="https://github.com/dmlc/mxnet">Github</a>
<span id="dropdown-menu-position-anchor-community">
<a aria-expanded="true" aria-haspopup="true" class="main-nav-link dropdown-toggle" data-toggle="dropdown" href="#" role="button">Community <span class="caret"></span></a>
<ul class="dropdown-menu navbar-menu" id="package-dropdown-menu-community">
<li><a class="main-nav-link" href="../../../community/index.html">Community</a></li>
<li><a class="main-nav-link" href="../../../community/contribute.html">Contribute</a></li>
<li><a class="main-nav-link" href="../../../community/powered_by.html">Powered By</a></li>
</ul>
</span>
<a class="main-nav-link" href="http://discuss.mxnet.io">Discuss</a>
<span id="dropdown-menu-position-anchor-version" style="position: relative"><a href="#" class="main-nav-link dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="true">Versions(0.12.0)<span class="caret"></span></a><ul id="package-dropdown-menu" class="dropdown-menu"><li><a class="main-nav-link" href=https://mxnet.incubator.apache.org/>1.0.0</a></li><li><a class="main-nav-link" href=https://mxnet.incubator.apache.org/versions/0.12.1/index.html>0.12.1</a></li><li><a class="main-nav-link" href=https://mxnet.incubator.apache.org/versions/0.12.0/index.html>0.12.0</a></li><li><a class="main-nav-link" href=https://mxnet.incubator.apache.org/versions/0.11.0/index.html>0.11.0</a></li><li><a class="main-nav-link" href=https://mxnet.incubator.apache.org/versions/master/index.html>master</a></li></ul></span></nav>
<script> function getRootPath(){ return "../../../" } </script>
<div class="burgerIcon dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#" role="button">☰</a>
<ul class="dropdown-menu" id="burgerMenu">
<li><a href="../../../install/index.html">Install</a></li>
<li><a class="main-nav-link" href="../../../tutorials/index.html">Tutorials</a></li>
<li class="dropdown-submenu">
<a href="#" tabindex="-1">Community</a>
<ul class="dropdown-menu">
<li><a href="../../../community/index.html" tabindex="-1">Community</a></li>
<li><a href="../../../community/contribute.html" tabindex="-1">Contribute</a></li>
<li><a href="../../../community/powered_by.html" tabindex="-1">Powered By</a></li>
</ul>
</li>
<li class="dropdown-submenu">
<a href="#" tabindex="-1">API</a>
<ul class="dropdown-menu">
<li><a href="../../../api/python/index.html" tabindex="-1">Python</a>
</li>
<li><a href="../../../api/scala/index.html" tabindex="-1">Scala</a>
</li>
<li><a href="../../../api/r/index.html" tabindex="-1">R</a>
</li>
<li><a href="../../../api/julia/index.html" tabindex="-1">Julia</a>
</li>
<li><a href="../../../api/c++/index.html" tabindex="-1">C++</a>
</li>
<li><a href="../../../api/perl/index.html" tabindex="-1">Perl</a>
</li>
</ul>
</li>
<li class="dropdown-submenu">
<a href="#" tabindex="-1">Docs</a>
<ul class="dropdown-menu">
<li><a href="../../../tutorials/index.html" tabindex="-1">Tutorials</a></li>
<li><a href="../../../faq/index.html" tabindex="-1">FAQ</a></li>
<li><a href="../../../architecture/index.html" tabindex="-1">Architecture</a></li>
<li><a href="https://github.com/apache/incubator-mxnet/tree/0.12.0/example" tabindex="-1">Examples</a></li>
<li><a href="../../../model_zoo/index.html" tabindex="-1">Model Zoo</a></li>
</ul>
</li>
<li><a href="../../../architecture/index.html">Architecture</a></li>
<li><a class="main-nav-link" href="https://github.com/dmlc/mxnet">Github</a></li>
<li id="dropdown-menu-position-anchor-version-mobile" class="dropdown-submenu" style="position: relative"><a href="#" tabindex="-1">Versions(0.12.0)</a><ul class="dropdown-menu"><li><a tabindex="-1" href=https://mxnet.incubator.apache.org/>1.0.0</a></li><li><a tabindex="-1" href=https://mxnet.incubator.apache.org/versions/0.12.1/index.html>0.12.1</a></li><li><a tabindex="-1" href=https://mxnet.incubator.apache.org/versions/0.12.0/index.html>0.12.0</a></li><li><a tabindex="-1" href=https://mxnet.incubator.apache.org/versions/0.11.0/index.html>0.11.0</a></li><li><a tabindex="-1" href=https://mxnet.incubator.apache.org/versions/master/index.html>master</a></li></ul></li></ul>
</div>
<div class="plusIcon dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#" role="button"><span aria-hidden="true" class="glyphicon glyphicon-plus"></span></a>
<ul class="dropdown-menu dropdown-menu-right" id="plusMenu"></ul>
</div>
<div id="search-input-wrap">
<form action="../../../search.html" autocomplete="off" class="" method="get" role="search">
<div class="form-group inner-addon left-addon">
<i class="glyphicon glyphicon-search"></i>
<input class="form-control" name="q" placeholder="Search" type="text"/>
</div>
<input name="check_keywords" type="hidden" value="yes"/>
<input name="area" type="hidden" value="default"/>
</form>
<div id="search-preview"></div>
</div>
<div id="searchIcon">
<span aria-hidden="true" class="glyphicon glyphicon-search"></span>
</div>
<!-- <div id="lang-select-wrap"> -->
<!-- <label id="lang-select-label"> -->
<!-- <\!-- <i class="fa fa-globe"></i> -\-> -->
<!-- <span></span> -->
<!-- </label> -->
<!-- <select id="lang-select"> -->
<!-- <option value="en">Eng</option> -->
<!-- <option value="zh">中文</option> -->
<!-- </select> -->
<!-- </div> -->
<!-- <a id="mobile-nav-toggle">
<span class="mobile-nav-toggle-bar"></span>
<span class="mobile-nav-toggle-bar"></span>
<span class="mobile-nav-toggle-bar"></span>
</a> -->
</div>
</div>
</div>
<script type="text/javascript">
$('body').css('background', 'white');
</script>
<div class="container">
<div class="row">
<div aria-label="main navigation" class="sphinxsidebar leftsidebar" role="navigation">
<div class="sphinxsidebarwrapper">
<ul class="current">
<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Python Documents</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="../index.html#ndarray-api">NDArray API</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="ndarray.html">NDArray API</a></li>
<li class="toctree-l3"><a class="reference internal" href="random.html">Random Distribution Generator NDArray API</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="">Linear Algebra NDArray API</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#overview">Overview</a></li>
<li class="toctree-l4"><a class="reference internal" href="#linear-algebra">Linear Algebra</a></li>
<li class="toctree-l4"><a class="reference internal" href="#api-reference">API Reference</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="sparse.html">Sparse NDArray API</a></li>
<li class="toctree-l3"><a class="reference internal" href="contrib.html">Contrib NDArray API</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#symbol-api">Symbol API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#module-api">Module API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#autograd-api">Autograd API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#gluon-api">Gluon API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#kvstore-api">KVStore API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#io-api">IO API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#image-api">Image API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#optimization-api">Optimization API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#callback-api">Callback API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#metric-api">Metric API</a></li>
<li class="toctree-l2"><a class="reference internal" href="../index.html#run-time-compilation-api">Run-Time Compilation API</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../r/index.html">R Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../julia/index.html">Julia Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../c++/index.html">C++ Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../scala/index.html">Scala Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../perl/index.html">Perl Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../faq/index.html">HowTo Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../architecture/index.html">System Documents</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../tutorials/index.html">Tutorials</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../../community/index.html">Community</a></li>
</ul>
</div>
</div>
<div class="content">
<div class="page-tracker"></div>
<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-python"><div class="highlight"><pre><span></span>// Single LQ factorization
A = [[1., 2., 3.], [4., 5., 6.]]
Q, L = gelqf(A)
Q = [[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]]
L = [[-3.74165739, 0.],
[-8.55235974, 1.96396101]]
// Batch LQ factorization
A = [[[1., 2., 3.], [4., 5., 6.]],
[[7., 8., 9.], [10., 11., 12.]]]
Q, L = gelqf(A)
Q = [[[-0.26726124, -0.53452248, -0.80178373],
[0.87287156, 0.21821789, -0.43643578]],
[[-0.50257071, -0.57436653, -0.64616234],
[0.7620735, 0.05862104, -0.64483142]]]
L = [[[-3.74165739, 0.],
[-8.55235974, 1.96396101]],
[[-13.92838828, 0.],
[-19.09768702, 0.52758934]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L528</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> (<em>NDArray, 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">NDArray 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>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 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-python"><div class="highlight"><pre><span></span>// Single matrix multiply-add
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
C = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
gemm(A, B, C, transpose_b=True, alpha=2.0, beta=10.0)
= [[14.0, 14.0, 14.0], [14.0, 14.0, 14.0]]
// Batch matrix multiply-add
A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
C = [[[10.0]], [[0.01]]]
gemm(A, B, C, transpose_b=True, alpha=2.0 , beta=10.0)
= [[[104.0]], [[0.14]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L68</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, optional, default=0</em>) – Multiply with transposed of first input (A).</li>
<li><strong>transpose_b</strong> (<em>boolean, optional, default=0</em>) – Multiply with transposed of second input (B).</li>
<li><strong>alpha</strong> (<em>double, optional, default=1</em>) – Scalar factor multiplied with A*B.</li>
<li><strong>beta</strong> (<em>double, optional, default=1</em>) – Scalar factor multiplied with C.</li>
<li><strong>out</strong> (<em>NDArray, 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">NDArray 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>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 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-python"><div class="highlight"><pre><span></span>// Single matrix multiply
A = [[1.0, 1.0], [1.0, 1.0]]
B = [[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [[4.0, 4.0, 4.0], [4.0, 4.0, 4.0]]
// Batch matrix multiply
A = [[[1.0, 1.0]], [[0.1, 0.1]]]
B = [[[1.0, 1.0]], [[0.1, 0.1]]]
gemm2(A, B, transpose_b=True, alpha=2.0)
= [[[4.0]], [[0.04 ]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L127</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, optional, default=0</em>) – Multiply with transposed of first input (A).</li>
<li><strong>transpose_b</strong> (<em>boolean, optional, default=0</em>) – Multiply with transposed of second input (B).</li>
<li><strong>alpha</strong> (<em>double, optional, default=1</em>) – Scalar factor multiplied with A*B.</li>
<li><strong>out</strong> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single matrix factorization
A = [[4.0, 1.0], [1.0, 4.25]]
potrf(A) = [[2.0, 0], [0.5, 2.0]]
// Batch matrix factorization
A = [[[4.0, 1.0], [1.0, 4.25]], [[16.0, 4.0], [4.0, 17.0]]]
potrf(A) = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L177</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> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single matrix inverse
A = [[2.0, 0], [0.5, 2.0]]
potri(A) = [[0.26563, -0.0625], [-0.0625, 0.25]]
// Batch matrix inverse
A = [[[2.0, 0], [0.5, 2.0]], [[4.0, 0], [1.0, 4.0]]]
potri(A) = [[[0.26563, -0.0625], [-0.0625, 0.25]],
[[0.06641, -0.01562], [-0.01562, 0,0625]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L235</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> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single matrix reduction
A = [[1.0, 1.0], [1.0, 7.0]]
sumlogdiag(A) = [1.9459]
// Batch matrix reduction
A = [[[1.0, 1.0], [1.0, 7.0]], [[3.0, 0], [0, 17.0]]]
sumlogdiag(A) = [1.9459, 3.9318]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L404</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> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single symmetric eigendecomposition
A = [[1., 2.], [2., 4.]]
U, L = syevd(A)
U = [[0.89442719, -0.4472136],
[0.4472136, 0.89442719]]
L = [0., 5.]
// Batch symmetric eigendecomposition
A = [[[1., 2.], [2., 4.]],
[[1., 2.], [2., 5.]]]
U, L = syevd(A)
U = [[[0.89442719, -0.4472136],
[0.4472136, 0.89442719]],
[[0.92387953, -0.38268343],
[0.38268343, 0.92387953]]]
L = [[0., 5.],
[0.17157288, 5.82842712]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L597</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> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single matrix multiply
A = [[1., 2., 3.], [4., 5., 6.]]
syrk(A, alpha=1., transpose=False)
= [[14., 32.],
[32., 77.]]
syrk(A, alpha=1., transpose=True)
= [[17., 22., 27.],
[22., 29., 36.],
[27., 36., 45.]]
// Batch matrix multiply
A = [[[1., 1.]], [[0.1, 0.1]]]
syrk(A, alpha=2., transpose=False) = [[[4.]], [[0.04]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L460</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, optional, default=0</em>) – Use transpose of input matrix.</li>
<li><strong>alpha</strong> (<em>double, optional, default=1</em>) – Scalar factor to be applied to the result.</li>
<li><strong>out</strong> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single triangular matrix multiply
A = [[1.0, 0], [1.0, 1.0]]
B = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
trmm(A, B, alpha=2.0) = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
// Batch triangular matrix multiply
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]], [[0.5, 0.5, 0.5], [0.5, 0.5, 0.5]]]
trmm(A, B, alpha=2.0) = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L292</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, optional, default=0</em>) – Use transposed of the triangular matrix</li>
<li><strong>rightside</strong> (<em>boolean, optional, default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</li>
<li><strong>alpha</strong> (<em>double, optional, default=1</em>) – Scalar factor to be applied to the result.</li>
<li><strong>out</strong> (<em>NDArray, 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">NDArray 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-python"><div class="highlight"><pre><span></span>// Single matrix solve
A = [[1.0, 0], [1.0, 1.0]]
B = [[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]]
trsm(A, B, alpha=0.5) = [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
// Batch matrix solve
A = [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.0, 1.0]]]
B = [[[2.0, 2.0, 2.0], [4.0, 4.0, 4.0]],
[[4.0, 4.0, 4.0], [8.0, 8.0, 8.0]]]
trsm(A, B, alpha=0.5) = [[[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]],
[[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]]
</pre></div>
</div>
<p>Defined in src/operator/tensor/la_op.cc:L355</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, optional, default=0</em>) – Use transposed of the triangular matrix</li>
<li><strong>rightside</strong> (<em>boolean, optional, default=0</em>) – Multiply triangular matrix from the right to non-triangular one.</li>
<li><strong>alpha</strong> (<em>double, optional, default=1</em>) – Scalar factor to be applied to the result.</li>
<li><strong>out</strong> (<em>NDArray, 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">NDArray or list of NDArrays</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<script>auto_index("api-reference");</script></div>
</div>
</div>
</div>
<div aria-label="main navigation" class="sphinxsidebar rightsidebar" role="navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="../../../index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Linear Algebra NDArray API</a><ul>
<li><a class="reference internal" href="#overview">Overview</a></li>
<li><a class="reference internal" href="#linear-algebra">Linear Algebra</a></li>
<li><a class="reference internal" href="#api-reference">API Reference</a></li>
</ul>
</li>
</ul>
</div>
</div>
</div><div class="footer">
<div class="section-disclaimer">
<div class="container">
<div>
<img height="60" src="https://raw.githubusercontent.com/dmlc/web-data/master/mxnet/image/apache_incubator_logo.png"/>
<p>
Apache MXNet is an effort undergoing incubation at The Apache Software Foundation (ASF), <strong>sponsored by the <i>Apache Incubator</i></strong>. Incubation is required of all newly accepted projects until a further review indicates that the infrastructure, communications, and decision making process have stabilized in a manner consistent with other successful ASF projects. While incubation status is not necessarily a reflection of the completeness or stability of the code, it does indicate that the project has yet to be fully endorsed by the ASF.
</p>
<p>
"Copyright © 2017, The Apache Software Foundation
Apache MXNet, MXNet, Apache, the Apache feather, and the Apache MXNet project logo are either registered trademarks or trademarks of the Apache Software Foundation."
</p>
</div>
</div>
</div>
</div> <!-- pagename != index -->
</div>
<script crossorigin="anonymous" integrity="sha384-0mSbJDEHialfmuBBQP6A4Qrprq5OVfW37PRR3j5ELqxss1yVqOtnepnHVP9aJ7xS" src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js"></script>
<script src="../../../_static/js/sidebar.js" type="text/javascript"></script>
<script src="../../../_static/js/search.js" type="text/javascript"></script>
<script src="../../../_static/js/navbar.js" type="text/javascript"></script>
<script src="../../../_static/js/clipboard.min.js" type="text/javascript"></script>
<script src="../../../_static/js/copycode.js" type="text/javascript"></script>
<script src="../../../_static/js/page.js" type="text/javascript"></script>
<script type="text/javascript">
$('body').ready(function () {
$('body').css('visibility', 'visible');
});
</script>
</body>
</html>