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<HTML><HEAD><TITLE>Newmat09 - SUE</TITLE></HEAD><BODY><H2>Safety, usability, efficiency</H2><A HREF="mat_arr.html"> next</A> -<A HREF="mat_arr.html"> skip</A> -<A HREF="design.html"> up</A> -<A HREF="index.html"> start</A><P><H3>Some general comments</H3>A library like <I>newmat</I> needs to balance <I>safety</I>,<I>usability</I> and <I>efficiency</I>.<P>By <B>safety</B>, I mean getting the right answer, and not causing crashes ordamage to the computer system.<P>By <B>usability</B>, I mean being easy to learn and use, including not being toocomplicated, being intuitive, saving the users' time, being nice to use.<P><B>Efficiency</B> means minimising the use of computer memory and time.<P>In the early days of computers the emphasis was on efficiency. But computerpower gets cheaper and cheaper, halving in price every 18 months. On the otherhand the unaided human brain is probably not a lot better than it was 100,000years ago!So we should expect the balance to shift to put more emphasis on safety andusability and a little less on efficiency.So I don't mind if my programs are a little less efficient than programswritten in pure C (or Fortran) if I gain substantially in safety and usability.But I would mind if they were a lot less efficient.<P><H3>Type of use</H3>Second reason for putting extra emphasis on safety and usability is the wayI and, I suspect, most other users actually use <I>newmat</I>. Most completed programsare used only a few times. Some result is required for a client, paper or thesis. Theprogram is developed and tested, the result is obtained, and the program archived.Of course bits of the program will be recycled for the next project. But it maybe less usual for the same program to be run over and over again. So the cost,computer time + people time, isin the development time and often, much less in the actual time to run the finalprogram. So good use of people time, especially during development is really important.This means you need highly usable libraries.<P>So if you are dealing with matrices, you want the good interface that I havetried to provide in <I>newmat</I>, and, of course, reliable methods underneath it.<P>Of course, efficiency is still important. We often want to run the biggest problemour computer will handle and often a little bigger. The C++ language almost letsus have both worlds. We can define a reasonably good interface, and get good efficiencyin the use of the computer.<P><H3>Levels of access</H3>We can imagine the <I>black box</I> model of a <I>newmat</I>. Suppose the insideis hidden but can be accessed by the methods described in the<A HREF="refer.html">reference</A> section. Then the interface is reasonablyconsistent and intuitive. Matrices can be accessed and manipulated in muchthe same way as doubles or ints in regular C. All accesses are checked. It ismost unlikely that an incorrect index will crash the system. In general, users donot need to use pointers, so one shouldn't get pointers pointing into space. And,hopefully, you will get simpler code and so less errors.<P>There are some exceptions to this. In particular, the<A HREF="elements.html">C-like subscripts</A> are not checked for validity. They givefaster access but with a lower level of safety.<P>Then there is the <A HREF="scalar.html">Store()</A> function which takes you to the dataarray within a matrix. This takes you right inside the <I>black box</I>. But this is whatyou have to use if you are writing, for example, a new matrix factorisation, andrequire fast access to the data array. I have tried to write code to simplify accessto the interior of a rectangular matrix, see file newmatrm.cpp, but I don't regard thisas very successful, as yet, and have not included it in the documentation. Ideally weshould have improved versions of this code for each of the major types of matrix. But,in reality, most of my matrix factorisations are written in what is basically the Clanguage with very little C++.<P>So our <I>box</I> is not very <I>black</I>. You have a choice of how far you penetrate.On the outside you have a good level of safety, but in some cases efficiency iscompromised a little. If you penetrate inside the <I>box</I> safety is reduced butyou can get better efficiency.<P><H3>Some performance data</H3>This section looks at the performance on <I>newmat</I> for simple sums, comparing itwith pure C code and with a somewhat unintelligent array program.<P>The following table lists the time (in seconds) for carrying out the operations<TT>X=A+B;</TT>, <TT>X=A+B+C;</TT>, <TT>X=A+B+C+D;</TT>, where <TT>X,A,B,C,D</TT>are of type ColumnVector, with a variety of programs.I am using Borland C++, version 5 in 32 bit console mode under windows NT 4.0on a PC with a 150 mhz pentium and 128 mbytes of memory.<PRE> length iters. newmat subs. C C-resz array X=A+B 2000000 2 1.2 3.7 1.2 1.4 3.3 200000 20 1.2 3.7 1.2 1.5 3.1 20000 200 1.0 3.6 1.0 1.2 2.9 2000 2000 1.0 3.6 0.9 0.9 2.2 200 20000 0.8 3.0 0.4 0.5 1.9 20 200000 5.5 2.9 0.4 0.9 2.8 2 2000000 43.9 3.2 1.0 4.2 12.3 X=A+B+C 2000000 2 2.5 4.6 1.6 2.1 32.5 200000 20 2.1 4.6 1.6 1.8 6.2 20000 200 1.8 4.5 1.5 1.8 5.6 2000 2000 1.8 4.4 1.3 1.3 3.9 200 20000 2.2 4.3 1.0 0.9 2.3 20 200000 8.5 4.3 1.0 1.2 3.0 2 2000000 62.5 3.9 1.0 4.4 17.7 X=A+B+C+D 2000000 2 3.7 6.7 2.4 2.8 260.7 200000 20 3.7 6.7 2.4 2.5 9.2 20000 200 3.4 6.6 2.3 2.9 8.2 2000 2000 2.9 6.4 2.0 2.0 5.9 200 20000 2.5 5.5 1.0 1.3 4.3 20 200000 9.9 5.5 1.0 1.6 4.5 2 2000000 76.5 5.8 1.7 5.0 24.9</PRE>The first column gives the lengths of the arrays, the second the numberof iterations and the remaining columns the total time required in seconds.If the only thing that consumed time was the double precision addition then thenumbers within each block of the table would be the same.<P>The column labelled <I>newmat</I> is using the standard <I>newmat</I> add. In thenext column the calculation is using the usual C style <I>for</I> loop and accessing theelements using <I>newmat</I> subscripts such as <TT>A(i)</TT>. The column labelled<I>C</I> uses the usual C method: <TT>while (j--) *x++ = *a++ + *b++;</TT> . Thefollowing column also includes an <TT>X.ReSize()</TT> in the outer loop to correspondto the reassignment of memory that <I>newmat</I> would do. The final column is thetime taken by a simple array package that makes no attempt to eliminate unnecessarycopying or to recycle temporary memory but does have array definitions of the basicoperators. It does, however, do its sums in blocks of 4 andcopies in blocks of 8 in the same way that <I>newmat</I> does. <P>Here are my conclusions.<UL><LI><I>Newmat</I> does very badly for length 2 and doesn't do very well for length20. There is some particularly tortuous code in <I>newmat</I> for determiningwhich sum algorithm to use and I am sure this could be improved. However the<I>array</I> program is also having difficulty with length 2 so it is unlikelythat the problem could be completely eliminated. <LI>The <I>array</I> program is running into problems for length 2,000,000. Thisis because RAM memory is being exhausted.<LI>For arrays of length 2000 or longer <I>newmat</I> is doing about as well as Cand slightly better than C with resize in the <TT>X=A+B</TT> table. For the other two tables itis slower, but not dramatically so.<LI>Addition using the <I>newmat</I> subscripts, while considerably slower than theothers, is still surprisingly good.<LI>The <I>array</I> program is more than 2 times slower than <I>newmat</I> for lengths2000 or higher.</UL>In summary: for the situation considered here, <I>newmat</I> is doing very wellfor large ColumnVectors, even for sums with several terms, but not so wellfor shorter ColumnVectors.<P><A HREF="mat_arr.html"> next</A> -<A HREF="mat_arr.html"> skip</A> -<A HREF="design.html"> up</A> -<A HREF="index.html"> start</A><P></BODY></HTML>⌨️ 快捷键说明
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