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<html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <!--This HTML is auto-generated from an M-file.To make changes, update the M-file and republish this document. --> <title>Converting a tensor to a matrix and vice versa</title> <meta name="generator" content="MATLAB 7.2"> <meta name="date" content="2007-01-10"> <meta name="m-file" content="B1_tenmat_doc"><style>body { background-color: white; margin:10px;}h1 { color: #990000; font-size: x-large;}h2 { color: #990000; font-size: medium;}/* Make the text shrink to fit narrow windows, but not stretch too far in wide windows. On Gecko-based browsers, the shrink-to-fit doesn't work. */ p,h1,h2,div.content div { /* for MATLAB's browser */ width: 600px; /* for Mozilla, but the "width" tag overrides it anyway */ max-width: 600px; /* for IE */ width:expression(document.body.clientWidth > 620 ? "600px": "auto" );}pre.codeinput { background: #EEEEEE; padding: 10px;}@media print { pre.codeinput {word-wrap:break-word; width:100%;}} span.keyword {color: #0000FF}span.comment {color: #228B22}span.string {color: #A020F0}span.untermstring {color: #B20000}span.syscmd {color: #B28C00}pre.codeoutput { color: #666666; padding: 10px;}pre.error { color: red;}p.footer { text-align: right; font-size: xx-small; font-weight: lighter; font-style: italic; color: gray;} </style></head> <body> <div class="content"> <h1>Converting a tensor to a matrix and vice versa</h1> <introduction> <p>We show how to convert a tensor to a matrix stored with extra information so that it can be converted back to a tensor. Converting to a matrix requies an ordered mapping of the tensor indices to the rows and the columns of the matrix. </p> </introduction> <h2>Contents</h2> <div> <ul> <li><a href="#1">Creating a tenmat (tensor as matrix) object</a></li> <li><a href="#5">Creating a tenmat by specifying the dimensions mapped to the rows</a></li> <li><a href="#6">Creating a tenmat by specifying the dimensions mapped to the columns</a></li> <li><a href="#7">Vectorize via tenmat</a></li> <li><a href="#8">Alternative ordering for the columns for mode-n matricization</a></li> <li><a href="#12">Constituent parts of a tenmat</a></li> <li><a href="#16">Creating a tenmat from its constituent parts</a></li> <li><a href="#17">Creating an empty tenmat</a></li> <li><a href="#18">Use double to convert a tenmat to a MATLAB matrix</a></li> <li><a href="#19">Use tensor to convert a tenmat to a tensor</a></li> <li><a href="#20">Use size and tsize for the dimensions of a tenmat</a></li> <li><a href="#21">Subscripted reference for a tenmat</a></li> <li><a href="#22">Subscripted assignment for a tenmat</a></li> <li><a href="#23">Use end for the last index</a></li> <li><a href="#24">Basic operations for tenmat</a></li> <li><a href="#30">Multiplying two tenmats</a></li> <li><a href="#32">Displaying a tenmat</a></li> </ul> </div> <h2>Creating a tenmat (tensor as matrix) object<a name="1"></a></h2><pre class="codeinput">X = tensor(1:24,[3 2 2 2]) <span class="comment">%<-- Create a tensor.</span></pre><pre class="codeoutput">X is a tensor of size 3 x 2 x 2 x 2 X(:,:,1,1) = 1 4 2 5 3 6 X(:,:,2,1) = 7 10 8 11 9 12 X(:,:,1,2) = 13 16 14 17 15 18 X(:,:,2,2) = 19 22 20 23 21 24</pre><pre class="codeinput">A = tenmat(X,[1 2],[3 4]) <span class="comment">%<-- Dims [1 2] map to rows, [3 4] to columns.</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 1 2 ] (modes of tensor corresponding to rows) A.cindices = [ 3 4 ] (modes of tensor corresponding to columns) A.data = 1 7 13 19 2 8 14 20 3 9 15 21 4 10 16 22 5 11 17 23 6 12 18 24</pre><pre class="codeinput">B = tenmat(X,[2 1],[3 4]) <span class="comment">%<-- Order matters!</span></pre><pre class="codeoutput">B is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 B.rindices = [ 2 1 ] (modes of tensor corresponding to rows) B.cindices = [ 3 4 ] (modes of tensor corresponding to columns) B.data = 1 7 13 19 4 10 16 22 2 8 14 20 5 11 17 23 3 9 15 21 6 12 18 24</pre><pre class="codeinput">C = tenmat(X,[1 2],[4 3]) <span class="comment">%<-- Order matters!</span></pre><pre class="codeoutput">C is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 C.rindices = [ 1 2 ] (modes of tensor corresponding to rows) C.cindices = [ 4 3 ] (modes of tensor corresponding to columns) C.data = 1 13 7 19 2 14 8 20 3 15 9 21 4 16 10 22 5 17 11 23 6 18 12 24</pre><h2>Creating a tenmat by specifying the dimensions mapped to the rows<a name="5"></a></h2> <p>If just the row indices are specified, then the columns are arranged in increasing order.</p><pre class="codeinput">A = tenmat(X,1) <span class="comment">%<-- Same as A = tenmat(X,1,2:4)</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 1 ] (modes of tensor corresponding to rows) A.cindices = [ 2 3 4 ] (modes of tensor corresponding to columns) A.data = 1 4 7 10 13 16 19 22 2 5 8 11 14 17 20 23 3 6 9 12 15 18 21 24</pre><h2>Creating a tenmat by specifying the dimensions mapped to the columns<a name="6"></a></h2> <p>Likewise, just the columns can be specified if the 3rd argument is a 't'. The rows are arranged in increasing order.</p><pre class="codeinput">A = tenmat(X, [2 3], <span class="string">'t'</span>) <span class="comment">%<-- Same as A = tenmat(X,[1 4],[2 3]).</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 1 4 ] (modes of tensor corresponding to rows) A.cindices = [ 2 3 ] (modes of tensor corresponding to columns) A.data = 1 4 7 10 2 5 8 11 3 6 9 12 13 16 19 22 14 17 20 23 15 18 21 24</pre><h2>Vectorize via tenmat<a name="7"></a></h2> <p>All the dimensions can be mapped to the rows or the columnns.</p><pre class="codeinput">A = tenmat(X,1:4,<span class="string">'t'</span>) <span class="comment">%<-- Map all the dimensions to the columns</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ ] (modes of tensor corresponding to rows) A.cindices = [ 1 2 3 4 ] (modes of tensor corresponding to columns) A.data = Columns 1 through 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Columns 15 through 24 15 16 17 18 19 20 21 22 23 24</pre><h2>Alternative ordering for the columns for mode-n matricization<a name="8"></a></h2> <p>Mode-n matricization means that only mode n is mapped to the rows. Different column orderings are available.</p><pre class="codeinput">A = tenmat(X,2) <span class="comment">%<-- By default, columns are ordered as [1 3 4].</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 2 ] (modes of tensor corresponding to rows) A.cindices = [ 1 3 4 ] (modes of tensor corresponding to columns) A.data = 1 2 3 7 8 9 13 14 15 19 20 21 4 5 6 10 11 12 16 17 18 22 23 24</pre><pre class="codeinput">A = tenmat(X,2,[3 1 4]) <span class="comment">%<-- Explicit specification.</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 2 ] (modes of tensor corresponding to rows) A.cindices = [ 3 1 4 ] (modes of tensor corresponding to columns) A.data = 1 7 2 8 3 9 13 19 14 20 15 21 4 10 5 11 6 12 16 22 17 23 18 24</pre><pre class="codeinput">A = tenmat(X,2,<span class="string">'fc'</span>) <span class="comment">%<-- Forward cyclic, i.e., [3 4 1].</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 2 ] (modes of tensor corresponding to rows) A.cindices = [ 3 4 1 ] (modes of tensor corresponding to columns) A.data = 1 7 13 19 2 8 14 20 3 9 15 21 4 10 16 22 5 11 17 23 6 12 18 24</pre><pre class="codeinput">A = tenmat(X,2,<span class="string">'bc'</span>) <span class="comment">%<-- Backward cyclic, i.e., [1 4 3].</span></pre><pre class="codeoutput">A is a matrix corresponding to a tensor of size 3 x 2 x 2 x 2 A.rindices = [ 2 ] (modes of tensor corresponding to rows) A.cindices = [ 1 4 3 ] (modes of tensor corresponding to columns) A.data = 1 2 3 13 14 15 7 8 9 19 20 21 4 5 6 16 17 18 10 11 12 22 23 24</pre><h2>Constituent parts of a tenmat<a name="12"></a></h2><pre class="codeinput">A.data <span class="comment">%<-- The matrix itself.</span></pre><pre class="codeoutput">ans = 1 2 3 13 14 15 7 8 9 19 20 21 4 5 6 16 17 18 10 11 12 22 23 24</pre><pre class="codeinput">A.tsize <span class="comment">%<-- Size of the original tensor.</span></pre><pre class="codeoutput">ans = 3 2 2 2</pre><pre class="codeinput">A.rdims <span class="comment">%<-- Dimensions that were mapped to the rows.</span></pre><pre class="codeoutput">ans = 2</pre><pre class="codeinput">A.cdims <span class="comment">%<-- Dimensions that were mapped to the columns.</span></pre><pre class="codeoutput">ans =⌨️ 快捷键说明
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