📄 triangle.html
字号:
<HTML><!-- -- Copyright (c) 1998,1999 -- University of Notre Dame -- -- Permission to use, copy, modify, distribute and sell this software -- and its documentation for any purpose is hereby granted without fee, -- provided that the above copyright notice appears in all copies and -- that both that copyright notice and this permission notice appear -- in supporting documentation. The University of Notre Dame makes no -- representations about the suitability of this software for any -- purpose. It is provided "as is" without express or implied warranty. -- --><HEAD><TITLE>Description of triangle</TITLE></HEAD><BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" ALINK="#ff0000"> <FONT FACE=Helvetica><!--end header--><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=2 WIDTH=100%><TR><TD><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=100%><TR><TD Align=left valign=middle width=440 rowspan=2><FONT FACE=verdana,arial,helvetica SIZE=+3 COLOR=#110088><B>triangle<int Uplo = dynamic_uplo></B></FONT></TD><TD valign=middle Align=right width=128 rowspan=2><A HREF="http://lsc.nd.edu/research/mtl"><IMG BORDER=0 SRC="./glossy-mtl-logo.jpg" height=48 ALT="[MTL Home]"></A></TD><TD Align=center width=280 nowrap><Font face=verdana,arial,helvetica size=+3><b>Programmers Guide</b></font></TD></TR><TR BGCOLOR='#2020b0'><TD HEIGHT=20 VALIGN='MIDDLE' NOWRAP align=center STYLE="font-family:verdana,arial,helvetica;font-weight:bold;"> <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./table_of_contents.html">Contents</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./mtl_index.html">Index</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="http://lsc.nd.edu/research/mtl/search.html">Search</A> </TD></TR></TABLE></TD></TR><TR><TD><Table Border=0 CellPadding=0 CellSpacing=0 width=100% cols=2><TR><TD Align=left><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "containers.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR><TR><TD><Img src = "selectors.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD><TD Align=right><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "type.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD></TR><TR><TD Align=left VAlign=top><b>Category</b>:containers,selectors</TD><TD Align=right VAlign=top><b>Component type</b>:type</TD></TR></Table></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Description</B></FONT></TD></TR><TR><TD> The triangular shape is a special case of the <A HREF="banded.html" >banded</A> shape. There are four kinds of triangular matrices in MTL, based on the <tt>Uplo</tt> argument: <table border=1> <tr> <td> Uplo type </td> <td> Sub </td> <td> Super </td> </tr> <tr> <td> upper </td> <td> 0 </td> <td> N - 1 </td> </tr> <tr> <td> unit_upper </td> <td> -1 </td> <td> N - 1 </td> </tr> <tr> <td> lower </td> <td> M - 1 </td> <td> 0 </td> </tr> <tr> <td> unit_lower </td> <td> M - 1 </td> <td> -1 </td> </tr> </table> The following is an example of a <tt><A HREF="triangle.html" >triangle</A><upper></tt> shaped <A HREF="matrix.html" >matrix</A>: <pre> [ 1 2 3 4 5 ] [ 0 6 7 8 9 ] [ 0 0 10 11 12 ] [ 0 0 0 13 14 ] [ 0 0 0 0 15 ] </pre> The next example is of a <tt><A HREF="triangle.html" >triangle</A><unit_lower></tt> <A HREF="matrix.html" >matrix</A>. The main <A HREF="diagonal.html" >diagonal</A> is not stored, since it consists of all ones. The MTL algorithms recognize when a <A HREF="matrix.html" >matrix</A> is ``unit'' and perform a slightly different operation to take this into account. The ones will not show up in an iteration of the <A HREF="matrix.html" >matrix</A>, and access to the A(i,i) element of a unit lower/upper <A HREF="matrix.html" >matrix</A> is an error. <pre> [ 1 0 0 0 0 ] [ 1 1 0 0 0 ] [ 2 3 1 0 0 ] [ 4 5 6 1 0 ] [ 7 8 9 10 1 ] </pre> Here are a couple examples of creating some triangular <A HREF="matrix.html" >matrix</A> types: <pre> typedef <A HREF="matrix.html" >matrix</A> < double, <A HREF="triangle.html" >triangle</A><upper>, <A HREF="banded.html" >banded</A><>, <A HREF="column_major.html" >column_major</A> >::type UpperTriangle; typedef <A HREF="matrix.html" >matrix</A> < double, <A HREF="triangle.html" >triangle</A><unit_lower>, <A HREF="packed.html" >packed</A><>, <A HREF="row_major.html" >row_major</A> >::type UnitLowerTriangle; </pre></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Example</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Definition</B></FONT></TD></TR><TR><TD><A HREF="../../mtl/matrix.h">matrix.h</A></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Template Parameters</B></FONT></TD></TR><TR><TD><BR><TABLE BORDER><TR><TH>Parameter</TH><TH>Description</TH><TH>Default</TH></TR><TR><TD><TT>Uplo</TT></TD><TD>The type of triangular <A HREF="matrix.html" >matrix</A>. Either upper, lower, unit_upper, or unit_lower.</TD><TD><TT> </TT></TD></TR></TABLE></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Model of</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Members</B></FONT></TD></TR><TR><TD><TABLE BORDER><TR><TH>Member</TH><TH>Where defined</TH><TH>Description</TH></TR> <TR><TD VALIGN="TOP"><TT> <TT>enum { id = TRI, uplo = Uplo, M=0, N=0 } </TT></TD> <TD><FONT FACE=Times SIZE=3> </FONT></TD> <TD><FONT FACE=Times SIZE=3> </FONT></TD> </TR></TABLE></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>New members</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Notes</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>See also</B></FONT></TD></TR><TR><TD></TD></TR></TABLE><!--start footer--> <P><CENTER><CENTER><IMG SRC="./blue-bar.jpg" width=640></CENTER></CENTER><P><A HREF="http://www.nd.edu"><IMG BORDER=0 SRC="./ndtoclogo.gif" ALT="[MTL Home]" ALIGN=absmiddle></A></A><FONT SIZE="-2"><A HREF="../LICENSE.htm">Copyright ©1998,1999 University of Notre Dame. All Rights Reserved.</FONT></FONT></BODY></HTML> ⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -