贝塞尔 函数 ( Bessel function, 又称柱函数 ) 是一类在各工程领域中有着广泛应用的特殊函数。贝塞尔函数是贝塞尔方程 ( 一个二阶常微分方程 ) 的解。 一般有三类贝塞尔函数 1 、第一类贝塞尔函数 (Bessel function of the first kind) J v (x) 2 、第二类贝塞尔函数 (Bessel function of the second kind), 又称诺依曼函数（ Neumann function ） :Y v (x)( 或 N v (x)) 3 、第三类贝塞尔函数（ Bessel function of the third kind ），又称汉克尔函数（ Hankel function ） : H 1 v (x) 和 H 2 v (x) 。 当贝塞尔方程为变形贝塞尔方程 ( 虚宗量贝塞尔方程 ) 时，方程的解一般有两类 1、 变形第一类贝塞尔函数（ modified Bessel function of the first kind ） I v (x) 2、 变形第二类贝塞尔函数（ modified Bessel function of the second kind ） K v (x) 另外应用比较多的函数还有球贝塞尔函数 (Spherical Bessel functions) 、艾里函数 (Airy functions ）等等。由于贝塞尔函数的广泛应用，很多软件都提供了现成的函数供用户使用。 Mathematics ：提供了比较多的 Bessel 函数。如： Bessel 函数 BesselJ BesselY BesselI BesselK 球体 Bessel 函数 SphericalBesselJ SphericalBesselY Hankel 函数 HankelH1 HankelH2 SphericalHankelH1 SphericalHankelH2 Airy 函数 AiryAi AiryAiPrime AiryBi AiryBiPrime Kelvin 函数 KelvinBer KelvinBei KelvinKer KelvinKei Struve 函数 StruveH StruveL AngerJ WeberE 零函数 BesselJZero BesselYZero AiryAiZero AiryBiZero Matlab ：提供了五个函数 besselj 、 bessely 、 besselh 、 besseli 和 besselk 分别对应第一类 Bessel 函数、第二类 Bessel 函数、第三类 Bessel 函数、第一类变形 Bessel 函数和第二类变形 Bessel 函数。语法 besselj(nu,z) ： nu 为函数的阶次，可以不为整数但必须为实数。 z 为函数的变量，可以为复数。还有 besselj(nu,z,1) 语法，可查询帮助。其他函数除了 besselh 有些不同外，基本类似。至于球函数、 Airy 函数等可通过这个函数来构造实现。 Excel ：提供了四个函数，即： BESSELJ 、 BESSELY 、 BESSELI 、 BESSELK 。 语法： BESSELJ (x,n) ；其中， x 为参数值， n 为函数的阶数。如果 n 非整数，则截尾取整。即 Excel 中只能计算整数阶次的 Bessel 函数。其他函数类似。 关于贝塞尔函数的专业书籍有： 中文 刘颖，《圆柱函数》国防工业出版社， 1983 。 奚定平，《贝塞尔函数》高等教育出版社和施普林格出版社， 1998. 英文 George Neville Watson 《 A Treatise on the Theory of Bessel Functions 》 Cambridge University Press ， 1995(1944 ， 1922) 最经典的一本书。 BG Korenev 《 Bessel Functions and Their Applications 》 CRC 2002. Milton Abramowitz, and Irene A. Stegun 《 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 》 Dover Publications 1964. I.S. Gradshteyn, I.M. Ryzhik, A Jeffrey, D Zwillinger 《 Table of integrals, series and products 》 (Seventh Edition) Academic Press 2007.
线性微分方程的求解方法很多，直接积分可以得到很高的精度。但是尝试一下用数值逼近的方法也是很有意思的。 下面以用Chebyshev多项式展开求解方程（x= 的一段） dy/dx=y y(0)=1 为例说明这个方法。 n阶Chebyshev定义为T(n,x)=cos(n arccos(x))。假设函数y(x)可以近似为 y(x)=\sum^{n}_{i=1} a_i T(i,x) 那么，取需要求解的区间内的n-1个点，加上初始条件，方程可以表示为n元线性方程组，用线性代数的方法可以求解展开系数a_i。 下面是实现这个方法的一段代码 function trychebyshev2(n,t0,t1)% use first n Chebyshev polinomial to approximate % t0:lower boundary; t1: upper boundary A=zeros(n,n); h=t0:(t1-t0)/n:t1; t=h(2:end); for j=1:n-1 for i=1:n A(j,i)=chebT(i,t(j))-chebQ(i,t(j)); % the differential equation is y'=y, y(0)=1 end end for i=1:n A(n,i)=chebT(i,0); end B=zeros(n,1); B(n)=1; x=linsolve(A,B); z=0:0.05:1; f1=0; for i=1:n f1=f1+x(i)*chebT(i,z); end f2=exp(z); plot(z,f1,'r',z,f2,'b'); function y=chebT(n,x) y=cos(n.*acos(x)); function y=chebQ(n,x) y=sin(n.*acos(x)).*n./sqrt(1-x.^2); 用5阶Chebyshev多项式时误差可以达到百分之几。 用10阶Chebyshev多项式近误差就小得多了。 不过，可以看到，在近似区间之外，近似函数和真实函数就完全不同了。
笔记（十一）IDL三维可视化的一种方法 用TV命令画等值面 pro three fitsname='../gaussfit.fits' a=mrdfits(fitsname) head=headfits(fitsname);read the header of the fits file to a vector nx = fxpar(head,'NAXIS1'); number of elements in the first dimension ny = fxpar(head,'NAXIS2'); nv = fxpar(head,'NAXIS3'); ;a=read_binary('/home/qianl/Software/idl_6.2/examples/data/head.dat',$ ; data_dims= ,data_type=1) b=lindgen(nx,ny,nv) bnz0=b/nx/ny bny0=(b-bnz0*nx*ny)/nx bnx0=b-bnz0*nx*ny-bny0*nx bx=bnx0*1.0d0 by=bny0*1.0d0 bv=bnz0*1.0d0 ;a=exp(-((bx-30.0)/10.0)^2-((by-30.0)/10.0)^2-((bv-30.0)/10.0)^2) shade_volume,a,max(a)/2.0,v,p,/low scale3,xrange= ,yrange= ,zrange= set_plot,'PS' filename='3d_TV.ps' ; set the file name of the output ps file device,file=filename,/COLOR, BITS=8 tv,polyshade(v,p,/t3d) device,/CLOSE end
笔记（十）二维高斯分布和高斯聚类的程序 生成两个二维高斯分布随机数样本的组合样本，用混合高斯模型聚类，算出每个点属于每个高斯成分的概率，代码如下，结果如图所示。 %testcluster.m: z1= ; z2= ; z= ; x=gmm(z,2); hold on scatter3(z(:,1),z(:,2),x(:,1),'.'); scatter3(z(:,1),z(:,2),x(:,2),'.'); %axis( ) %view( ); view(-162,-13); hold off print -dpng gmm.png %gmm.m function varargout = gmm(X, K_or_centroids) % ============================================================ % Expectation-Maximization iteration implementation of % Gaussian Mixture Model. % % PX = GMM(X, K_OR_CENTROIDS) % = GMM(X, K_OR_CENTROIDS) % % - X: N-by-D data matrix. % - K_OR_CENTROIDS: either K indicating the number of % components or a K-by-D matrix indicating the % choosing of the initial K centroids. % % - PX: N-by-K matrix indicating the probability of each % component generating each point. % - MODEL: a structure containing the parameters for a GMM: % MODEL.Miu: a N-by-K matrix. % MODEL.Sigma: a D-by-D-by-K matrix. % MODEL.Pi: a 1-by-K vector. % ============================================================ threshold = 1e-15; = size(X); if isscalar(K_or_centroids) % judge if K_or_centroids is a scalar K = K_or_centroids; % K is the number of Gaussian components % randomly pick centroids rndp = randperm(N); % randomly permute the index array 1:N centroids = X(rndp(1:K), :); % centers of the Gaussian components else K = size(K_or_centroids, 1); % size of the first dimension (number of rows) centroids = K_or_centroids; end % initial values = init_params(); Lprev = -inf; while true Px = calc_prob(); % new value for pGamma pGamma = Px .* repmat(pPi, N, 1); % (N by K) matrix pGamma = pGamma ./ repmat(sum(pGamma, 2), 1, K); % (N by K) matrix % new value for parameters of each Component Nk = sum(pGamma, 1); % add to a single row (1 by K) pMiu = diag(1./Nk) * pGamma' * X; % (K by D) pPi = Nk/N; for kk = 1:K Xshift = X-repmat(pMiu(kk, :), N, 1); % (N by D) pSigma(:, :, kk) = (Xshift'* ... (diag(pGamma(:, kk)) * Xshift))/ Nk(kk); % (D by D) end % check for convergence L = sum(log(Px*pPi')); if L-Lprev threshold break; end Lprev = L; end if nargout == 1 varargout = {Px}; else model = = init_params() pMiu = centroids; % set the centers of Gaussian components pPi = zeros(1, K); pSigma = zeros(D, D, K); % hard assign x to each centroids distmat = repmat(sum(X.*X, 2), 1, K) + ... repmat(sum(pMiu.*pMiu, 2)', N, 1) - ...% (N by K) matrix 2*X*pMiu'; % pMiu' (D by K) % add the columns to a single column % and creat a large % matrix (N by K) by % tiling % X*pMiu' (N by K) % distmat is an (N by K) % to specify the % distance of every data % point to the K centers = min(distmat, [], 2); % return minimum of every row % labels is the column % numbers for k=1:K Xk = X(labels == k, :); pPi(k) = size(Xk, 1)/N; pSigma(:, :, k) = cov(Xk); % if Xk is a vector, cov(Xk)is % the variance,just set the % K initial (D by D matrix) to the same value end end function Px = calc_prob() Px = zeros(N, K); for k = 1:K Xshift = X-repmat(pMiu(k, :), N, 1); % N by D matrix inv_pSigma = inv(pSigma(:, :, k)); % invert the matrix (D by D) tmp = sum((Xshift*inv_pSigma) .* Xshift, 2); % N element vector coef = (2*pi)^(-D/2) * sqrt(det(inv_pSigma)); Px(:, k) = coef * exp(-0.5*tmp); % the probability end end end
笔记（七）关于命令行直接运行IDL脚本 假设有一个IDL脚本test.pro，内容为 pro test print,1+1 end 现在想直接在shell里运行而不先启动IDL，怎么办？我的土办法是另写一个文件test，内容为 #!/usr/local/idl test 再变为可执行文件。然后，把test.pro里的pro test和end两行注释掉。这样就可以直接敲test了。IDL自动启动，运行test.pro。 如果想执行完直接退出IDL，那么在test.pro中再加一行 exit 就可以了。
笔记（五）模拟中性氢质量函数 在这里附上模拟某个极限流量时观测到的河外星系中性氢的质量函数的代码。 z=0.1; %redshift rmax=zD(z);% maximum distance corresponding to maximum redshift thetastar=8.6e-3;% normalization of the mass function V=200.0; % line width in km/s f=0.7; % factor accounting for the line shape Slim=3.0e-5; % flux limit, in Jy dx=3.906; % length of side of a volume element, in Mpc dy=3.906; dz=3.906; volume=dx*dy*dz; % volume element, in Mpc^3 local=26.0; % local latitude dec1=local+30.0; % range of relevant declination dec2=local-30.0; %a=load('densmap_250_G10.0.dat'); x=a(:,1); % coordinate y=a(:,2); z=a(:,3); b=a(:,4); % % %max(b); % % %maxb=23.5072;% the maximum of the density contrast % % b=b./maxb; % = meshgrid(-250:1:250, -250:1:250, -250:1:250); % % v = x .* exp(-x.^2 - y.^2 - z.^2); % slice(x,y,z,a, ,2, ) n=length(b); MHI= ; NHI=zeros(1,5); M=6:10; M=M+0.5; for i=1:n if mod(i,1000)==0 i end V=sgc2ec(x(i),y(i),z(i)); ra=V(1); dec=V(2); r=sqrt(x(i).^2+y(i).^2+z(i).^2); if decdec1decdec2rrmax % if in the right dec and redshift range ngal=volume*(b(i)+1.0)*thetastar; if ngal~=0 mgal=floor(ngal); xgal=mgal+((ngal-mgal)rand());% if the number is not integer % the decimal part is treated as % probability if xgal0 temp=GenRanNum2(xgal); % generate a sample with the distribution of the mass function for i=1:xgal S=temp(i)./(2.356e5.*r.^2.*V.*f); if SSlim % if can be detected MHI= ; % add to the whole sample Dist= ; j=ceil(log10(temp(i))-6); NHI(j)=NHI(j)+1; end end end end end end save simulation_NHI.txt NHI -ascii %plot(M,NHI,'*'); bar(M,NHI); % histogram title(strcat('redshift:',num2str(z),' Slim:',num2str(Slim))); xlabel('\fontname{times New Toman}\fontsize{16}log(M_{HI}/M_{sun})'); ylabel('\fontname{times New Toman}\fontsize{16}N'); print -depsc2 simulation.eps
红移距离转换也是常用的一个操作。现把代码放在下面 function y=zD(z) % z-distance relation, distance in units of Mpc h=0.72; DH=3000./h; % in Mpc OmegaM=0.274; OmegaLam=0.726; %fun=strcat('',num2str(OmegaM),'*(1+x)^3+',num2str(OmegaLam),'') DC=DH.*comdis(OmegaM,OmegaLam,z); DM=DC; % for zero curvature y=DM.*(1+z); %================================================= function y=comdis(OmegaM,OmegaLam,z0) function f=E(z) f=1.0./sqrt(OmegaM.*(1+z).^3+OmegaLam); end y=quadl(@E,0,z0); end
语录：101条伟大的计算机编程名言 HACKER 2009-05-23 18:50 阅读 17 评论 1 字号： 大 大 中 中 小 小 人们总是害怕改变。电被发明出来的时候他们害怕电，是不是？他们害怕煤，害怕蒸汽机车。无知无所不在，并导致恐惧。但随着时间推移，人们终究会接受最新的科技。 正如比尔盖茨曾经警告过一样，计算机已经真正成为我们的最新科技，几乎遍布我们日常生活的每一方面。所以，我们这个时代的某些最伟大的头脑开始思索起计算机和软件对于人类的重要性来了。以下就是101条有关计算机的伟大名言，并且，既然我们这个网站是一个软件开发网站，我们尤其关注编程方面的。 计算机 1、计算机没什么用。他们只会告诉你答案。 (巴勃罗毕加索，画家) 2、计算机就跟比基尼一样，省去了人们许多的胡思乱想。 (萨姆尤因，作家) 3、他们拥有计算机，他们也还可能拥有其他的大规模杀伤性武器。 (珍内特雷诺，美国前女司法部长) 4、跟计算机工作酷就酷在这里，它们不会生气，能记住所有东西，还有，它们不会喝光你的啤酒。 (保罗利里，吉他手) 5、如果汽车能赶上计算机的发展周期的话，一辆今天的劳斯莱斯仅值100美元，每加仑要跑100万英里，每年还得爆炸一次，把里面的人杀个精光。 (RobertX.Cringely，技术作家) 计算机智能 6、计算机总是越来越智能的。科学家告诉我们说不久它们就能跟我们对话了。（这里的它们，我指的是计算机。我怀疑科学家永远都不能跟我们对话。） (DaveBarry，幽默作家) 7、我最近注意到，在共同文化中，那种对计算机变得智能化并最终掌控世界的妄想恐惧症几乎彻底消失了。据我所知，这跟MS-DOS的发布基本是同步的。 (LarryDeLuca) 8、计算机会不会思考这个问题就像问潜水艇会不会游泳一样。 (EdsgerW.Dijkstra，图灵奖获得者) 9、活了一百年却只能记住30M字节是荒谬的。你知道，这比一张压缩盘还要少。人类境况正在变得日趋退化。 (MarvinMinsky，人工智能研究的奠基人) 信任 10、这座城市的中央计算机告诉你的？R2D2，你不该相信一台陌生的计算机！ (C3PO，星球大战中的翻译机器人) 11、永远不要相信一台不能扔掉一扇窗户*的计算机 (斯蒂夫沃兹尼亚克，苹果联合创始人) *译者：暗指微软的wINDOWS操作系统 硬件 12、硬件:计算机系统中可被踢的部分。 (JeffPesis) 软件 13、今天大部分的软件都很像上百万块砖堆叠在一起组成的埃及金字塔，缺乏结构完整性，只能靠强力和成千上万的奴隶完成。 (阿伦凯，图灵奖获得者，面向对象创始人) 14、我终于明白向上兼容性是怎么回事了。这是指我们得保留所有原有错误。 (DennievanTassel) 操作系统 15、有两样重要产品出自伯克利：LSD和BSD*。我们不相信这是个巧合。 (JeremyS.Anderson) *译者：LSD是一种药力至强的迷幻剂，BSD-BSD（BerkeleySoftwareDistribution，伯克利软件套件）是Unix的衍生系统 16、2038年1月19日，凌晨3点14分07秒 (UNIX中的世界末日*1970年1月1号之后的2^32秒) *译者：word跟world同音，UNIX用4个字节（WORD）表示时间，所以最多只能计时2^32秒 17、每个操作系统都差不多我们都一样的烂。 (微软的高级副总裁布莱恩瓦伦蒂尼这样描述操作系统的安全状况，2003) 18、微软有出了个新版本，WindowsXP,据大家说是有史以来最稳定的Windows，对我而言,这就好像是在说芦笋是有史以来发音最清脆的蔬菜一样 (DaveBarry) 互联网 19、互联网？那个东西还在吗？ (HomerSimpson) 20、网络就像是个母夜叉。我每转到一处都会看见小个的按钮命令我提交*。 (Nytwind) *译者注：Submit：提交，另一层意思是要求屈服 21、想想看吧，已经有一百万只猴子坐在一百万台打字机旁，可Usenet就是比不上莎士比亚。 (BlairHoughton) 软件产业 22、计算机软件产业最为惊人的成就，是其持续不断地放弃硬件产业的惊人成果和稳定性。 (HenryPetroski) 23、真正的创新经常来自于那些贴近市场、但无力拥有市场的的小型初创公司。 (TimmMartin) 24、人们常说，伟大的科学学科就像是站在其它巨人肩膀上的巨人。人们也说过，软件产业正如站在其他侏儒脚上的侏儒。 (AlanCooper，交互设计之父) 25、这无关比特、字节和协议，而关乎利润和损益。 (郭士纳，IBM前CEO) 26、我们是微软。反抗是徒劳的。你会被同化的。 (保险杠贴纸) 软件演示 27、不管演示在彩排的时候有多好，一旦在观众面前展示时，演示不出错的几率与观众人数成反比，与投入的金钱总额成正比。 (MarkGibbs) 软件专利 28、专利大多数都是垃圾。浪费时间去阅读这些专利是愚蠢的。只有专利持有人才会这么干，还得强迫自己才会看。 (LinusTorvalds，LINUX创始人) 复杂性 29、控制复杂性是计算机编程的本质。 (BrianKernigan) 30、复杂性杀死一切。它把程序员的生活给搞砸了，它令产品难以规划、创建和测试，带来了安全挑战，并导致最终用户和管理员沮丧不已。 (RayOzzie) 31、进行软件设计有两种方式。一种是让它尽量简单，让人看不出明显的不足。另一种是弄得尽量复杂，让人看不出明显的缺陷。 (C.A.R.Hoare) 32、好的软件的作用是让复杂的东西看起来简单。 (GradyBooch，UML创始人之一) 易用性 33、不管那些计算机书籍如何宣称，只需记住，你并非傀儡。真正的傀儡是那些无法设计出易于使用的硬件和软件的那些人，尽管他们是技术专家，因为这是普通消费者赖以生活的东西。 (WalterMossberg，科技专栏记者) 34、软件供应商在努力尝试让他们的软件更易于操作迄今为止，他们最好的办法就是翻出所有的老手册，然后在封面盖上易于操作这几个字。 (比尔盖茨) 35、有个老套的故事说有人希望他的计算机能像他的电话机一样好用。他的愿望实现了，因为我已经不知道该如何使用自己的电话了。 (BjarneStroustrup，C++之父) 用户 36、任何一个傻瓜都会用电脑。很多都会。 (TedNelson) 37、只有两个行业把客户称为用户*。 (EdwardTufte，信息设计大师) *译者注：一个是计算机设计，另一个是毒品交易，computerdesignanddrugdealing 程序员 38、程序员在跟宇宙赛跑，他们在努力开发出更大更好的傻瓜程序，而宇宙则努力培养出更大更好的白痴。到目前为止，宇宙领先。 (RichCook) 39、你们当中很多人都知道程序员的美德。当然啦，有三种：那就是懒惰、急躁以及傲慢。 (LarryWall，Perl发明者) 40、程序员的问题是你无法预料他在做什么，直到为时已晚。 (SeymourCray，超级计算机之父) 41、那就是这些自认为痛恨计算机的人的真实面目。他们实际上真正痛恨的是糟糕的程序员。 (拉瑞尼文，科幻作家) 42、很长时间以来我一直困惑不已，为什么一些又贵又先进的东西会一点用都没有。直到我突然想起，计算机不就是一台愚蠢之至却拥有难以置信的做聪明事能力的机器嘛，而程序员不就是聪明绝顶却拥有难以置信的干蠢事的能力的人嘛。一句话，他们简直就是天生绝配。 (比尔布莱森，旅游文学作家) 43、不像学学涂涂画画也能让某人成为专家级画家，计算机科学教育不会让任何人成为一名编程大师。 (埃里克雷蒙，开源运动领袖) 44、一个程序员是经历以下事情后仍能证明自己是严格的专家的人：他可以历经数不清的捶打，可取材于无关紧要的文档，用上面的争议数据作出模糊假设，并以此计算出测微精度的无数片面理解的答案,并由一个不可靠、脑袋充满质疑、公开宣称要让一个倒霉透顶、没有指望、毫无防备,要求第一时间获得信息的部门狼狈不堪、令人生厌的人使用一台准确度有问题的仪器去实施。 (IEEE网格新闻杂志) 45、运气好的黑客能用几个月的时间-生产出一个小规模的开发团体（比如说，7-8人）历尽艰辛一起工作了一年多才能做出来的东西。IBM经常报告说某些程序员的生产力要比其它工人高百倍，甚至更多。 (PeterSeebach，黑客) 46、最好的程序员跟好的程序员相比可不止好那么一点点。这种好不是一个数量级的，取决于标准怎么定：概念创造性、速度、设计的独创性或者解决问题的能力。 (兰德尔E斯特劳斯，科技作家) 47、伟大的车工值得给他几倍于普通车工的薪水，但一个伟大的软件代码作家，其价值则要等同于一个普通的软件写手的价格的1万倍。 (比尔盖茨) 编程 48、就算它工作不正常也别担心。如果一切正常，你早该失业了。 (Mosher的软件工程定律) 49、靠代码行数来衡量开发进程就好比用重量来衡量飞机制造的进度。 (比尔盖茨) 50、写代码的社会地位比盗墓的高，比管理的低。 (杰拉尔德温伯格，软件与系统思想家) 51、首先学习计算机科学及理论。接着形成自己编程的风格。然后把这一切都忘掉，尽管改程序就是了。 (GeorgeCarrette，杰出软件工程师,开源推广者) 52、先解决问题再写代码。 (JohnJohnson) 53、乐观主义是编程行业的职业病；用户反馈则是治疗方法。 (KentBeck) 54、迭代者为人，递归者为神。 (L.PeterDeutsch) 55、布尔值最好的一点是，就算你错了，也顶多错了一位而已。 (无名氏) 56、数组的下标是从0开始好还是从1开始好呢？我的0.5的折衷方案，以我之见，没有经过适当考虑就被否决掉了。 (StanKelly-Bootle) 编程语言 57、只有两种编程语言：一种是天天挨骂的，另一种是没人用的。 (BjarneStroustrup，C++之父) 58、PHP是不合格的业余爱好者创建的，他们犯做了个小恶；Perl是娴熟而堕落的专家创建的，他们犯了阴险狡诈的大恶。 (JonRibbens) 59、COBOL的使用摧残大脑；其教育应被视为刑事犯罪。 (E.W.Dijkstra) 60、把良好的编程风格教给那些之前曾经接触过BASIC的学生几乎是不可能的。作为可能的程序员，他们已精神残废，无重塑的可能了。 (E.W.Dijkstra) 61、我想微软之所以把它叫做.Net，是因为这样它就不会在Unix的目录里显示出来了。 (Oktal) 62、Thereisnoprogramminglanguagenomatterhowstructuredthatwillpreventprogrammersfrommakingbadprograms. (LarryFlon) 63、计算机语言设计犹如在公园里漫步。我是说侏罗纪公园。 (LarryWall) C/C++ 64、搞了50年的编程语言的研究，我们难道就以C++告终啦？ (RichardA.OKeefe) 65、写C或者C++就像是在用一把卸掉所有安全防护装置的链锯。 (BobGray) 66、在C++里你想搬起石头砸自己的脚更为困难了，不过一旦你真的做了，整条腿都要报销。 (BjarneStroustrup) 67、C++:友人可造访你的私有成员之地也。 (GavinRussellBaker) 译者：Friends：C++的友元，是一种定义在类外部的普通函数，但它需要在类体内进行说明，为了与该类的成员函数加以区别，在说明时前面加以关键字friend。友元不是成员函数，但是它可以访问类中的私有成员。友元的作用在于提高程序的运行效率，但是，它破坏了类的封装性和隐藏性，使得非成员函数可以访问类的私有成员。 68、罗马帝国灭亡的其中一个主要原因是他们没有0-这样他们就没法给自己的C程序指明成功退出的路径了。 (RobertFirth) Java 69、Java从许多方面来说就是C++。 (MichaelFeldman) 70、说Java好就好在运行于多个操作系统之上，就好像说肛交好就好在不管男女都行。 (Alanna) 71、好吧，Java也许是编程语言的好榜样。但Java应用则是应用程序的坏榜样。 (pixadel) 72、要是Java真的有垃圾回收的话，大部分程序在执行的时候就会把自己干掉了。 (RobertSewell) 开源 73、软件就像性事：免费/自由更好。 (LinusTorvalds) 74、唯一对免费软件感到害怕的人，是自己的产品还要不值钱的人。 (DavidEmery) 代码 75、好代码本身就是最好的文档。 (SteveMcConnell) 76、你自己的代码如果超过6个月不看，再看的时候也一样像是别人写的。 (伊格尔森定律) 77、前面90%的代码要占用开发时间的前90%。剩下的10%的代码要占用开发时间的另一90%。 (TomCargill) 软件开发 78、好的程序员会用脑，但是好的向导救我们于样样都要想到。 (FrancisGlassborow) 79、在软件里面，我们鲜有有意义的需求。就算有，衡量成功的唯一尺度也取决于我们的解决方案是否解决了客户对问题是什么的观念的转变。 (JeffAtwood) 80、想想我们计算机程序的糟糕现状吧，很显然软件开发仍是黑箱艺术，还不能称之为工程学科。 (BillClinton，前美国总统) 81、没有伟大的团队就没有伟大的软件，可大部分的软件团队举止就像是支离破碎的家庭。 (吉姆麦卡锡，微软VC++总监) 调试 82、一旦我们开始编程，就会惊讶地发现让程序正常没想象中那么简单。调试不可避免。那一刻我认记忆犹新，当时我就意识到，从今往后我生活的大部分时间都要花在寻找自己程序的错误上面了。 (莫里斯威尔克斯调试探索,1949) 83、调试难度本来就是写代码的两倍。因此，如果你写代码的时候聪明用尽，根据定义，你就没有能耐去调试它了。 (BrianKernighan) 84、如果调试是除虫的过程，那么编程就一定是把臭虫放进来的过程。 (EdsgerW.Dijkstra) 质量 85、我才不管它能不能在你的机器上运行呢！我们又没装到你的机器上！ (VidiuPlaton，罗马尼亚的微软最佳学生合作伙伴MSP) 86、编程就像性一样：一时犯错，终生维护。 (MichaelSinz) 87、有两种写出无错程序的办法；只有第三种有用。 (AlanJ.Perlis) 88、软件质量与指针算法不可兼得。 (BertrandMeyer) 89、如果麦当劳像软件公司那样运作的话，每一百个巨无霸就会有一个令你食物中毒，而他们的回应是，真对不起，这是一张额外附送两个的赠券。 (MarkMinasi) 90、永远要这样写代码，好像最终维护你代码的人是个狂暴的、知道你住在哪里的精神病患者。 (MartinGolding) 91、是人都会犯错，不过要想把事情彻底搞砸还得请电脑出马。 (PaulEhrlich) 92、计算机比人类历史上的任何发明都更快速地导致你犯更多的错误可能除了手枪和龙舌兰酒是例外。 (MitchRadcliffe) 预测 93、能发明的东西都发明出来了。 (查尔斯杜埃尔,美国专利局局长，1899年) 94、我认为全球市场约需5台计算机。 (托马斯沃森,IBM董事长,约1948年) 95、看上去我们已经到达了利用计算机技术可能获得的极限了，尽管下这样的结论得小心，因为不出五年这听起来就会相当愚蠢。 (约翰冯诺伊曼,约1949年) 96、但这又有什么好处呢？ (IBM先进计算机系统部的工程师对微芯片的评论,1968年) 97、我们没有理由让每一个人在家都拥有一台电脑。 (肯奥尔森,数据设备公司（DEC）总裁，1977年) 98、640K对每一个人来说都已足够。 (比尔盖茨,1981年) 99、WindowsNT的RAM寻址空间可达2G，这比任何应用程序所需都要多。 (微软,谈及WindowsNT的开发时所言,1992年) 100、我们永远也无法真正成为无纸化社会，直到掌上电脑一族发布擦我1.0*（WipeMe1.0）为止。 (安迪皮尔逊，商界领袖) *译者注：意思是说难道你大便不用纸吗？ 101、长此以往，除了按键的手指外，人类的肢体将全部退化。 (弗兰克劳埃德赖特，建筑师) 附：英文版 2009 - 05 - 24 101 Great Computer Programming Quotes 关键字: 精彩转载 People always fear change. People feared electricity when it was invented, didnt they? People feared coal, they feared gas-powered engines. There will always be ignorance, and ignorance leads to fear. But with time, people will come to accept their silicon masters. As Bill Gates once warned, computers have indeed become our silicon masters, pervading nearly every aspect of our modern lives. As a result, some of the greatest minds of our time have pondered the significance of computers and software on the human condition. Following are 101 great quotes about computers, with an emphasis on programming, since after all this is a software development site. Computers Computers are useless. They can only give you answers. (Pablo Picasso) Computers are like bikinis. They save people a lot of guesswork. (Sam Ewing) They have computers, and they may have other weapons of mass destruction. (Janet Reno) Thats whats cool about working with computers. They dont argue, they remember everything, and they dont drink all your beer. (Paul Leary) If the automobile had followed the same development cycle as the computer, a Rolls-Royce would today cost $100, get a million miles per gallon, and explode once a year, killing everyone inside. (Robert X. Cringely) Computer Intelligence Computers are getting smarter all the time. Scientists tell us that soon they will be able to talk to us. (And by they, I mean computers. I doubt scientists will ever be able to talk to us.) (Dave Barry) Ive noticed lately that the paranoid fear of computers becoming intelligent and taking over the world has almost entirely disappeared from the common culture. Near as I can tell, this coincides with the release of MS-DOS. (Larry DeLuca) The question of whether computers can think is like the question of whether submarines can swim. (Edsger W. Dijkstra) Its ridiculous to live 100 years and only be able to remember 30 million bytes. You know, less than a compact disc. The human condition is really becoming more obsolete every minute. (Marvin Minsky) Trust The citys central computer told you? R2D2, you know better than to trust a strange computer! (C3PO) Never trust a computer you cant throw out a window. (Steve Wozniak) Hardware Hardware: The parts of a computer system that can be kicked. (Jeff Pesis) Software Most software today is very much like an Egyptian pyramid with millions of bricks piled on top of each other, with no structural integrity, but just done by brute force and thousands of slaves. (Alan Kay) Ive finally learned what upward compatible means. It means we get to keep all our old mistakes. (Dennie van Tassel) Operating Systems There are two major products that come out of Berkeley: LSD and UNIX. We dont believe this to be a coincidence. (Jeremy S. Anderson) 19 Jan 2038 at 3:14:07 AM (End of the word according to Unix2^32 seconds after January 1, 1970) Every operating system out there is about equal We all suck. (Microsoft senior vice president Brian Valentine describing the state of the art in OS security, 2003) Microsoft has a new version out, Windows XP, which according to everybody is the most reliable Windows ever. To me, this is like saying that asparagus is the most articulate vegetable ever. (Dave Barry) Internet The Internet? Is that thing still around? (Homer Simpson) The Web is like a dominatrix. Everywhere I turn, I see little buttons ordering me to Submit. (Nytwind) Come to think of it, there are already a million monkeys on a million typewriters, and Usenet is nothing like Shakespeare. (Blair Houghton) Software Industry The most amazing achievement of the computer software industry is its continuing cancellation of the steady and staggering gains made by the computer hardware industry. (Henry Petroski) True innovation often comes from the small startup who is lean enough to launch a market but lacks the heft to own it. (Timm Martin) It has been said that the great scientific disciplines are examples of giants standing on the shoulders of other giants. It has also been said that the software industry is an example of midgets standing on the toes of other midgets. (Alan Cooper) It is not about bits, bytes and protocols, but profits, losses and margins. (Lou Gerstner) We are Microsoft. Resistance Is Futile. You Will Be Assimilated. (Bumper sticker) Software Demos No matter how slick the demo is in rehearsal, when you do it in front of a live audience, the probability of a flawless presentation is inversely proportional to the number of people watching, raised to the power of the amount of money involved. (Mark Gibbs) Software Patents The bulk of all patents are crap. Spending time reading them is stupid. Its up to the patent owner to do so, and to enforce them. (Linus Torvalds) Complexity Controlling complexity is the essence of computer programming. (Brian Kernigan) Complexity kills. It sucks the life out of developers, it makes products difficult to plan, build and test, it introduces security challenges, and it causes end-user and administrator frustration. (Ray Ozzie) There are two ways of constructing a software design. One way is to make it so simple that there are obviously no deficiencies. And the other way is to make it so complicated that there are no obvious deficiencies. (C.A.R. Hoare) The function of good software is to make the complex appear to be simple. (Grady Booch) Ease of Use Just remember: youre not a dummy, no matter what those computer books claim. The real dummies are the people whothough technically expertcouldnt design hardware and software thats usable by normal consumers if their lives depended upon it. (Walter Mossberg) Software suppliers are trying to make their software packages more user-friendly Their best approach so far has been to take all the old brochures and stamp the words user-friendly on the cover. (Bill Gates) Theres an old story about the person who wished his computer were as easy to use as his telephone. That wish has come true, since I no longer know how to use my telephone. (Bjarne Stroustrup) Users Any fool can use a computer. Many do. (Ted Nelson) There are only two industries that refer to their customers as users. (Edward Tufte) Programmers Programmers are in a race with the Universe to create bigger and better idiot-proof programs, while the Universe is trying to create bigger and better idiots. So far the Universe is winning. (Rich Cook) Most of you are familiar with the virtues of a programmer. There are three, of course: laziness, impatience, and hubris. (Larry Wall) The trouble with programmers is that you can never tell what a programmer is doing until its too late. (Seymour Cray) Thats the thing about people who think they hate computers. What they really hate is lousy programmers. (Larry Niven) For a long time it puzzled me how something so expensive, so leading edge, could be so useless. And then it occurred to me that a computer is a stupid machine with the ability to do incredibly smart things, while computer programmers are smart people with the ability to do incredibly stupid things. They are, in short, a perfect match. (Bill Bryson) Computer science education cannot make anybody an expert programmer any more than studying brushes and pigment can make somebody an expert painter. (Eric Raymond) A programmer is a person who passes as an exacting expert on the basis of being able to turn out, after innumerable punching, an infinite series of incomprehensive answers calculated with micrometric precisions from vague assumptions based on debatable figures taken from inconclusive documents and carried out on instruments of problematical accuracy by persons of dubious reliability and questionable mentality for the avowed purpose of annoying and confounding a hopelessly defenseless department that was unfortunate enough to ask for the information in the first place. (IEEE Grid newsmagazine) A hacker on a roll may be able to producein a period of a few monthssomething that a small development group (say, 7-8 people) would have a hard time getting together over a year. IBM used to report that certain programmers might be as much as 100 times as productive as other workers, or more. (Peter Seebach) The best programmers are not marginally better than merely good ones. They are an order-of-magnitude better, measured by whatever standard: conceptual creativity, speed, ingenuity of design, or problem-solving ability. (Randall E. Stross) A great lathe operator commands several times the wage of an average lathe operator, but a great writer of software code is worth 10,000 times the price of an average software writer. (Bill Gates) Programming Dont worry if it doesnt work right. If everything did, youd be out of a job. (Moshers Law of Software Engineering) Measuring programming progress by lines of code is like measuring aircraft building progress by weight. (Bill Gates) Writing code has a place in the human hierarchy worth somewhere above grave robbing and beneath managing. (Gerald Weinberg) First learn computer science and all the theory. Next develop a programming style. Then forget all that and just hack. (George Carrette) First, solve the problem. Then, write the code. (John Johnson) Optimism is an occupational hazard of programming; feedback is the treatment. (Kent Beck) To iterate is human, to recurse divine. (L. Peter Deutsch) The best thing about a boolean is even if you are wrong, you are only off by a bit. (Anonymous) Should array indices start at 0 or 1? My compromise of 0.5 was rejected without, I thought, proper consideration. (Stan Kelly-Bootle) Programming Languages There are only two kinds of programming languages: those people always bitch about and those nobody uses. (Bjarne Stroustrup) PHP is a minor evil perpetrated and created by incompetent amateurs, whereas Perl is a great and insidious evil perpetrated by skilled but perverted professionals. (Jon Ribbens) The use of COBOL cripples the mind; its teaching should therefore be regarded as a criminal offense. (E.W. Dijkstra) It is practically impossible to teach good programming style to students that have had prior exposure to BASIC. As potential programmers, they are mentally mutilated beyond hope of regeneration. (E. W. Dijkstra) I think Microsoft named .Net so it wouldnt show up in a Unix directory listing. (Oktal) There is no programming languageno matter how structuredthat will prevent programmers from making bad programs. (Larry Flon) Computer language design is just like a stroll in the park. Jurassic Park, that is. (Larry Wall) C/C++ Fifty years of programming language research, and we end up with C++? (Richard A. OKeefe) Writing in C or C++ is like running a chain saw with all the safety guards removed. (Bob Gray) In C++ its harder to shoot yourself in the foot, but when you do, you blow off your whole leg. (Bjarne Stroustrup) C++ : Where friends have access to your private members. (Gavin Russell Baker) One of the main causes of the fall of the Roman Empire was thatlacking zerothey had no way to indicate successful termination of their C programs. (Robert Firth) Java Saying that Java is nice because it works on all OSes is like saying that anal sex is nice because it works on all genders. (Alanna) Fine, Java MIGHT be a good example of what a programming language should be like. But Java applications are good examples of what applications SHOULDNT be like. (pixadel) If Java had true garbage collection, most programs would delete themselves upon execution. (Robert Sewell) Open Source Software is like sex: Its better when its free. (Linus Torvalds) The only people who have anything to fear from free software are those whose products are worth even less. (David Emery) Code Good code is its own best documentation. (Steve McConnell) Any code of your own that you havent looked at for six or more months might as well have been written by someone else. (Eaglesons Law) The first 90% of the code accounts for the first 90% of the development time. The remaining 10% of the code accounts for the other 90% of the development time. (Tom Cargill) Software Development Good programmers use their brains, but good guidelines save us having to think out every case. (Francis Glassborow) In software, we rarely have meaningful requirements. Even if we do, the only measure of success that matters is whether our solution solves the customers shifting idea of what their problem is. (Jeff Atwood) Considering the current sad state of our computer programs, software development is clearly still a black art, and cannot yet be called an engineering discipline. (Bill Clinton) You cant have great software without a great team, and most software teams behave like dysfunctional families. (Jim McCarthy) Debugging As soon as we started programming, we found to our surprise that it wasnt as easy to get programs right as we had thought. Debugging had to be discovered. I can remember the exact instant when I realized that a large part of my life from then on was going to be spent in finding mistakes in my own programs. (Maurice Wilkes discovers debugging, 1949) Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you areby definitionnot smart enough to debug it. (Brian Kernighan) If debugging is the process of removing bugs, then programming must be the process of putting them in. (Edsger W. Dijkstra) Quality I dont care if it works on your machine! We are not shipping your machine! (Vidiu Platon) Programming is like sex: one mistake and youre providing support for a lifetime. (Michael Sinz) There are two ways to write error-free programs; only the third one works. (Alan J. Perlis) You can either have software quality or you can have pointer arithmetic, but you cannot have both at the same time. (Bertrand Meyer) If McDonalds were run like a software company, one out of every hundred Big Macs would give you food poisoning, and the response would be, Were sorry, heres a coupon for two more. (Mark Minasi) Always code as if the guy who ends up maintaining your code will be a violent psychopath who knows where you live. (Martin Golding) To err is human, but to really foul things up you need a computer. (Paul Ehrlich) A computer lets you make more mistakes faster than any invention in human historywith the possible exceptions of handguns and tequila. (Mitch Radcliffe) Predictions Everything that can be invented has been invented. (Charles H. Duell, Commissioner, U.S. Office of Patents, 1899) I think theres a world market for about 5 computers. (Thomas J. Watson, Chairman of the Board, IBM, circa 1948) It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years. (John Von Neumann, circa 1949) But what is it good for? (Engineer at the Advanced Computing Systems Division of IBM, commenting on the microchip, 1968) There is no reason for any individual to have a computer in his home. (Ken Olson, President, Digital Equipment Corporation, 1977) 640K ought to be enough for anybody. (Bill Gates, 1981) Windows NT addresses 2 Gigabytes of RAM, which is more than any application will ever need. (Microsoft, on the development of Windows NT, 1992) We will never become a truly paper-less society until the Palm Pilot folks come out with WipeMe 1.0 . (Andy Pierson) If it keeps up, man will atrophy all his limbs but the push-button finger. (Frank Lloyd Wright)
22条经典的编程引言 HACKER 2009-05-24 15:08 阅读 51 评论 6 字号： 大 大 中 中 小 小 下面的这些经典的引言来自英文，也许有些我翻译的是不很好，所以，我提供了中英对照，如果有问题，请大家指正。 过早的优化是万恶之源。Premature optimization is the root of all evil! - Donald Knuth 在水里行走和以一个需求规格进行软件开发，有一点是相同的，那就是如果水或需求都被冻住不了，那么行走和软件开发都会变得容易。Walking on water and developing software from a specification are easy if both are frozen - Edward V Berard Hofstadter 定理：一件事情总是会花费比你预期更多的时间，就算是你已经考虑过本条Hofstadter 定理。It always takes longer than you expect, even when you take into account Hofstadters Law. - Hofstadters Law 有些遇到问题的人总是会说我知道，我会使用正则表达式，那么，你现在有两个问题了。（意思是：你本想用正则表达式来解决你已有问题，但实际上你又引入了正则表达式的一个新问题）Some people, when confronted with a problem, think I know, Ill use regular expressions. Now they have two problems - Jamie Zawinski 调试程序的难度是写代码的两倍。因此，只要你的代码写的尽可能的清楚，那么你在调试代码时就不需要那么地有技巧。Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it. - Brian Kernighan 用代码行来衡量开发进度，无异于用重量来衡量制造飞机的进度。Measuring programming progress by lines of code is like measuring aircraft building progress by weight. - Bill Gates PHP被一些不合格的业余人员造就成了一个小恶魔；而Perl则是被一些熟练的但不正当的专业人员造就成了一个超级大恶魔。PHP is a minor evil perpetrated and created by incompetent amateurs, whereas Perl is a great and insidious evil, perpetrated by skilled but perverted professionals. - Jon Ribbens 在两个场合我被问到：请你告诉我，如果你给机器输入了错误的数字，那么，是否还能得到正确的答案？我并不能正确领会这类想法。（意思是：程序需要有纠错的能力吗？）On two occasions I have been asked, Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out? I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. - Charles Babbage 在编程的时候，我们一定要想像一下，以后维护我们自己的代码的那个人会成为一个强烈的精神病人，并且，他还知道我们住在哪里？Always code as if the guy who ends up maintaining your code will be a violent psychopath who knows where you live. - Rick Osborne 现代的编程是程序员努力建一个更大更傻的程序和世界正在尝试创造更多更傻的人之间的一种竞赛，目前为止，后者是赢家。Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning. - Rich Cook 我才不关于我的代码是否能在你的机器上工作！我们不会给你提供机器。I dont care if it works on your machine! We are not shipping your machine! - Ovidiu Platon 我总是希望我的电脑能够像电话一样容易使用；我的这个希望正在变成现实，因为我现在已经不知道怎么去使用我的电话了。I have always wished for my computer to be as easy to use as my telephone; my wish has come true because I can no longer figure out how to use my telephone. - Bjarne Stroustrup 计算机是一种在人类历史上所有发明中，可以让你比以前更快地犯更多的错误的发明，同样，其也包括了手枪和龙舌兰酒这两种发明的缺陷。A computer lets you make more mistakes faster than any other invention in human history, with the possible exceptions of handguns and tequila. - Mitch Ratcliffe 如果调试程序是一种标准的可以铲除BUG的流程，那么，编程就是把他们放进来的流程。If debugging is the process of removing software bugs, then programming must be the process of putting them in. - E. W. Dijkstra 教一群被BASIC先入为主的学生，什么是好的编程风格简直是一件不可能的事。对于一些有潜力的程序员，他们所受到的智力上的伤害远远超过了重建他们的信心。It is practically impossible to teach good programming style to students that have had prior exposure to BASIC. As potential programmers, they are mentally mutilated beyond hope of regeneration. - E. W. Dijkstra 理论上来说，理论和实际是一样的。但实际上来说，他们则不是。In theory, theory and practice are the same. In practice, theyre not. - Unknown 只有两个事情是无穷尽的：宇宙和人类的愚蠢。当然，我现在还不能确定宇宙是无穷尽的。Two things are infinite: the universe and human stupidity; and Im not sure about the universe. - Albert Einstein Perl这种语言就好像是被RSA加密算法加密过的一样。Perl - The only language that looks the same before and after RSA encryption. - Keith Bostic 我爱最终期限，我喜欢嗖嗖嗖的声音就像他们在飞一样。I love deadlines. I like the whooshing sound they make as they fly by. - Douglas Adams 说Java好的是因为它跨平台就像好像说肛交好是因为其可以适用于一切性别。Saying that Java is good because it works on all platforms is like saying **** sex is good because it works on all genders - Unknown XML就像是一种强暴如果它不能解决你的问题，那只能说明你没有用好它。XML is like violence - if it doesnt solve your problems, you are not using enough of it. - Unknown 爱因期坦说，自然界中的一切一定会有一个简单的解释，因为上帝并不是反复无常和独裁的。当然，不会有什么信仰能程序员像爱因期坦那样感到舒服。Einstein argued that there must be simplified explanations of nature, because God is not capricious or arbitrary. No such faith comforts the software engineer. - Fred Brooks
标签: 编程
