<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <html> <!-- Created by GNU Texinfo 6.5, http://www.gnu.org/software/texinfo/ --> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <title>Basics (GNU Octave (version 5.1.0))</title> <meta name="description" content="Basics (GNU Octave (version 5.1.0))"> <meta name="keywords" content="Basics (GNU Octave (version 5.1.0))"> <meta name="resource-type" content="document"> <meta name="distribution" content="global"> <meta name="Generator" content="makeinfo"> <link href="index.html#Top" rel="start" title="Top"> <link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index"> <link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> <link href="Sparse-Matrices.html#Sparse-Matrices" rel="up" title="Sparse Matrices"> <link href="Storage-of-Sparse-Matrices.html#Storage-of-Sparse-Matrices" rel="next" title="Storage of Sparse Matrices"> <link href="Sparse-Matrices.html#Sparse-Matrices" rel="prev" title="Sparse Matrices"> <style type="text/css"> <!-- a.summary-letter {text-decoration: none} blockquote.indentedblock {margin-right: 0em} blockquote.smallindentedblock {margin-right: 0em; font-size: smaller} blockquote.smallquotation {font-size: smaller} div.display {margin-left: 3.2em} div.example {margin-left: 3.2em} div.lisp {margin-left: 3.2em} div.smalldisplay {margin-left: 3.2em} div.smallexample {margin-left: 3.2em} div.smalllisp {margin-left: 3.2em} kbd {font-style: oblique} pre.display {font-family: inherit} pre.format {font-family: inherit} pre.menu-comment {font-family: serif} pre.menu-preformatted {font-family: serif} pre.smalldisplay {font-family: inherit; font-size: smaller} pre.smallexample {font-size: smaller} pre.smallformat {font-family: inherit; font-size: smaller} pre.smalllisp {font-size: smaller} span.nolinebreak {white-space: nowrap} span.roman {font-family: initial; font-weight: normal} span.sansserif {font-family: sans-serif; font-weight: normal} ul.no-bullet {list-style: none} --> </style> <link rel="stylesheet" type="text/css" href="octave.css"> </head> <body lang="en"> <a name="Basics"></a> <div class="header"> <p> Next: <a href="Sparse-Linear-Algebra.html#Sparse-Linear-Algebra" accesskey="n" rel="next">Sparse Linear Algebra</a>, Up: <a href="Sparse-Matrices.html#Sparse-Matrices" accesskey="u" rel="up">Sparse Matrices</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p> </div> <hr> <a name="Creation-and-Manipulation-of-Sparse-Matrices"></a> <h3 class="section">22.1 Creation and Manipulation of Sparse Matrices</h3> <p>The size of mathematical problems that can be treated at any particular time is generally limited by the available computing resources. Both, the speed of the computer and its available memory place limitation on the problem size. </p> <p>There are many classes of mathematical problems which give rise to matrices, where a large number of the elements are zero. In this case it makes sense to have a special matrix type to handle this class of problems where only the nonzero elements of the matrix are stored. Not only does this reduce the amount of memory to store the matrix, but it also means that operations on this type of matrix can take advantage of the a priori knowledge of the positions of the nonzero elements to accelerate their calculations. </p> <p>A matrix type that stores only the nonzero elements is generally called sparse. It is the purpose of this document to discuss the basics of the storage and creation of sparse matrices and the fundamental operations on them. </p> <table class="menu" border="0" cellspacing="0"> <tr><td align="left" valign="top">• <a href="Storage-of-Sparse-Matrices.html#Storage-of-Sparse-Matrices" accesskey="1">Storage of Sparse Matrices</a>:</td><td> </td><td align="left" valign="top"> </td></tr> <tr><td align="left" valign="top">• <a href="Creating-Sparse-Matrices.html#Creating-Sparse-Matrices" accesskey="2">Creating Sparse Matrices</a>:</td><td> </td><td align="left" valign="top"> </td></tr> <tr><td align="left" valign="top">• <a href="Information.html#Information" accesskey="3">Information</a>:</td><td> </td><td align="left" valign="top"> </td></tr> <tr><td align="left" valign="top">• <a href="Operators-and-Functions.html#Operators-and-Functions" accesskey="4">Operators and Functions</a>:</td><td> </td><td align="left" valign="top"> </td></tr> </table> </body> </html>