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<HTML><!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"><!-- Created on October, 14 2005 by texi2html 1.64 --><!-- Written by: Lionel Cons <Lionel.Cons@cern.ch> (original author) Karl Berry <karl@freefriends.org> Olaf Bachmann <obachman@mathematik.uni-kl.de> and many others.Maintained by: Olaf Bachmann <obachman@mathematik.uni-kl.de>Send bugs and suggestions to <texi2html@mathematik.uni-kl.de> --><HEAD><TITLE>Blitz++: Indirection</TITLE><META NAME="description" CONTENT="Blitz++: Indirection"><META NAME="keywords" CONTENT="Blitz++: Indirection"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><META NAME="Generator" CONTENT="texi2html 1.64"></HEAD><BODY LANG="" BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#0000FF" VLINK="#800080" ALINK="#FF0000"><A NAME="SEC127"></A><TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0><TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_5.html#SEC126"> < </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC128"> > </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> << </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top"> Up </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> >> </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD></TR></TABLE><H1> 6. Indirection </H1><!--docid::SEC127::--><P><A NAME="IDX319"></A><A NAME="IDX320"></A></P><P><STRONG>Indirection</STRONG> is the ability to modify or access an array at a set ofselected index values. Blitz++ provides several forms of indirection: </P><P><UL><LI><STRONG>Using a list of array positions</STRONG>: this approach is usefulif you need to modify an array at a set of scattered points.<P><LI><STRONG>Cartesian-product indirection</STRONG>: as an example, for atwo-dimensional array you might have a list <CODE>I</CODE> of rows and a list<CODE>J</CODE> of columns, and you want to modify the array at all (i,j) positionswhere i is in <CODE>I</CODE> and j is in <CODE>J</CODE>. This is a <STRONG>cartesianproduct</STRONG> of the index sets <CODE>I</CODE> and <CODE>J</CODE>.<P><LI><STRONG>Over a set of strips</STRONG>: for efficiency, you can represent anarbitrarily-shaped subset of an array as a list of one-dimensional strips.This is a useful way of handling <STRONG>Regions Of Interest</STRONG> (ROIs).<P></UL><P><center> <CENTER><IMG SRC="indirect.gif" ALT="indirect"></CENTER></center><center> Three styles of indirection. <A NAME="DOCF4" HREF="blitz_fot.html#FOOT4">(4)</A></center></P><P><A NAME="IDX321"></A></P><P>In all cases, Blitz++ expects a Standard Template Library container. Someuseful STL containers are <CODE>list<></CODE>, <CODE>vector<></CODE>, <CODE>deque<></CODE> and<CODE>set<></CODE>. Documentation of these classes is often provided with yourcompiler, or see also the good documentation at<A HREF="http://www.sgi.com/Technology/STL/">http://www.sgi.com/Technology/STL/</A>. STL containers are used becausethey are widely available and provide easier manipulation of "sets" thanBlitz++ arrays. For example, you can easily expand and merge sets which arestored in STL containers; doing this is not so easy with Blitz++ arrays,which are designed for numerical work.</P><P>STL containers are generally included by writing</P><P><TABLE><tr><td> </td><td class=example><pre>#include <list> // for list<>#include <vector> // for vector<>#include <deque> // for deque<>#include <set> // for set<></pre></td></tr></table></P><P><A NAME="IDX322"></A></P><P>The <CODE>[]</CODE> operator is overloaded on arrays so that the syntax<CODE>array[container]</CODE> provides an indirect view of the array. So far,this indirect view may only be used as an lvalue (i.e. on the left-hand sideof an assignment statement).</P><P>The examples in the next sections are available in the Blitz++ distributionin <TT>`<examples/indirect.cpp>'</TT>.</P><P><HR SIZE="6"><A NAME="SEC128"></A><TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0><TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> < </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC129"> > </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> << </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> Up </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> >> </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD></TR></TABLE><H2> 6.1 Indirection using lists of array positions </H2><!--docid::SEC128::--><P><A NAME="IDX323"></A><A NAME="IDX324"></A></P><P>The simplest kind of indirection uses a list of points. For one-dimensionalarrays, you can just use an STL container of integers. Example:</P><P><TABLE><tr><td> </td><td class=example><pre> Array<int,1> A(5), B(5); A = 0; B = 1, 2, 3, 4, 5; vector<int> I; I.push_back(2); I.push_back(4); I.push_back(1); A[I] = B;</pre></td></tr></table></P><P>After this code, the array A contains <CODE>[ 0 2 3 0 5 ]</CODE>.</P><P>Note that arrays on the right-hand-side of the assignment must have the sameshape as the array on the left-hand-side (before indirection). In thestatement <CODE>A[I] = B</CODE>, A and B must have the same shape, not I and B.</P><P>For multidimensional arrays, you can use an STL container of<CODE>TinyVector<int,N_rank></CODE> objects. Example:</P><P><TABLE><tr><td> </td><td class=example><pre> Array<int,2> A(4,4), B(4,4); A = 0; B = 10*tensor::i + tensor::j; typedef TinyVector<int,2> coord; list<coord> I; I.push_back(coord(1,1)); I.push_back(coord(2,2)); A[I] = B;</pre></td></tr></table></P><P>After this code, the array A contains:</P><P><TABLE><tr><td> </td><td class=example><pre> 0 0 0 0 0 11 0 0 0 0 22 0 0 0 0 0</pre></td></tr></table></P><P>(The <CODE>tensor::i</CODE> notation is explained in the section on indexplaceholders <A HREF="blitz_3.html#SEC88">3.6 Index placeholders</A>).</P><P><HR SIZE="6"><A NAME="SEC129"></A><TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0><TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC128"> < </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC130"> > </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC130"> << </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> Up </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> >> </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD></TR></TABLE><H2> 6.2 Cartesian-product indirection </H2><!--docid::SEC129::--><P><A NAME="IDX325"></A><A NAME="IDX326"></A></P><P>The Cartesian product of the sets I, J and K is the set of (i,j,k) tuplesfor which i is in I, j is in J, and k is in K. </P><P>Blitz++ implements cartesian-product indirection using an <STRONG>adaptor</STRONG>which takes a set of STL containers and iterates through their Cartesianproduct. Note that the cartesian product is never explicitly created. Youcreate the Cartesian-product adaptor by calling the function:</P><P><TABLE><tr><td> </td><td class=example><pre>template<class T_container>indexSet(T_container& c1, T_container& c2, ...)</pre></td></tr></table></P><P>The returned adaptor can then be used in the <CODE>[]</CODE> operator of an arrayobject.</P><P>Here is a two-dimensional example:</P><P><A NAME="IDX327"></A></P><P><TABLE><tr><td> </td><td class=example><pre> Array<int,2> A(6,6), B(6,6); A = 0; B = 10*tensor::i + tensor::j; vector<int> I, J; I.push_back(1); I.push_back(2); I.push_back(4); J.push_back(0); J.push_back(2); J.push_back(5); A[indexSet(I,J)] = B;</pre></td></tr></table></P><P>After this code, the A array contains:</P><P><TABLE><tr><td> </td><td class=example><pre> 0 0 0 0 0 010 0 12 0 0 1520 0 22 0 0 25 0 0 0 0 0 040 0 42 0 0 45 0 0 0 0 0 0</pre></td></tr></table></P><P>All the containers used in a cartesian product must be the same type (e.g.all <CODE>vector<int></CODE> or all <CODE>set<TinyVector<int,2> ></CODE>), but they maybe different sizes. Singleton containers (containers containing a singlevalue) are fine.</P><P><HR SIZE="6"><A NAME="SEC130"></A><TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0><TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC129"> < </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> > </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> << </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> Up </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> >> </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD></TR></TABLE><H2> 6.3 Indirection with lists of strips </H2><!--docid::SEC130::--><P><A NAME="IDX328"></A><A NAME="IDX329"></A></P><P>You can also do indirection with a container of one-dimensional<STRONG>strips</STRONG>. This is useful when you want to manipulate somearbitrarily-shaped, well-connected subdomain of an array. By representingthe subdomain as a list of strips, you allow Blitz++ to operate on vectors,rather than scattered points; this is much more efficient.</P><P><A NAME="IDX330"></A></P><P>Strips are represented by objects of type <CODE>RectDomain<N></CODE>, where<CODE>N</CODE> is the dimensionality of the array. The <CODE>RectDomain<N></CODE> classcan be used to represent any rectangular subdomain, but for indirection itis only used to represent strips.</P><P>You create a strip by using this function:</P><P><A NAME="IDX331"></A></P><P><TABLE><tr><td> </td><td class=example><pre>RectDomain<N> strip(TinyVector<int,N> start, int stripDimension, int ubound);</pre></td></tr></table></P><P>The <CODE>start</CODE> parameter is where the strip starts; <CODE>stripDimension</CODE>is the dimension in which the strip runs; <CODE>ubound</CODE> is the last indexvalue for the strip. For example, to create a 2-dimensional strip from(2,5) to (2,9), one would write:</P><P><TABLE><tr><td> </td><td class=example><pre>TinyVector<int,2> start(2,5);RectDomain<2> myStrip = strip(start,secondDim,9);</pre></td></tr></table></P><P>Here is a more substantial example which creates a list of stripsrepresenting a circle subset of an array:</P><P><TABLE><tr><td> </td><td class=example><pre> const int N = 7; Array<int,2> A(N,N), B(N,N); typedef TinyVector<int,2> coord; A = 0; B = 1; double centre_i = (N-1)/2.0; double centre_j = (N-1)/2.0; double radius = 0.8 * N/2.0; // circle will contain a list of strips which represent a circular // subdomain. list<RectDomain<2> > circle; for (int i=0; i < N; ++i) { double jdist2 = pow2(radius) - pow2(i-centre_i); if (jdist2 < 0.0) continue; int jdist = int(sqrt(jdist2)); coord startPos(i, int(centre_j - jdist)); circle.push_back(strip(startPos, secondDim, int(centre_j + jdist))); } // Set only those points in the circle subdomain to 1 A[circle] = B;</pre></td></tr></table></P><P>After this code, the A array contains:</P><P><TABLE><tr><td> </td><td class=example><pre> 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0</pre></td></tr></table></P><P><A NAME="TinyVector"></A><HR SIZE="6"><TABLE CELLPADDING=1 CELLSPACING=1 BORDER=0><TR><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_6.html#SEC127"> << </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_7.html#SEC131"> >> </A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT"> <TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz.html#SEC_Top">Top</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_toc.html#SEC_Contents">Contents</A>]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[Index]</TD><TD VALIGN="MIDDLE" ALIGN="LEFT">[<A HREF="blitz_abt.html#SEC_About"> ? </A>]</TD></TR></TABLE><BR> <FONT SIZE="-1">This document was generatedby <I>Julian Cummings</I> on <I>October, 14 2005</I>using <A HREF="http://www.mathematik.uni-kl.de/~obachman/Texi2html"><I>texi2html</I></A></BODY></HTML>⌨️ 快捷键说明
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